Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 04/2019, Volume 2019, Issue 749, pp. 161 - 200

Severi varieties and Brill–Noether theory of curves on K3 surfaces are well understood...

EXISTENCE | MATHEMATICS | HILBERT SCHEME | LINEAR SERIES | FAMILIES | COMPONENTS | RATIONAL CURVES | EXPECTED NUMBER | SINGULAR CURVES | MODULI | SYZYGY CONJECTURE

EXISTENCE | MATHEMATICS | HILBERT SCHEME | LINEAR SERIES | FAMILIES | COMPONENTS | RATIONAL CURVES | EXPECTED NUMBER | SINGULAR CURVES | MODULI | SYZYGY CONJECTURE

Journal Article

Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2014, Volume 193, Issue 4, pp. 961 - 973

A separating ( $$M-2$$ )-curve is a smooth geometrically irreducible real projective curve $$X$$ such that $$X(\mathbb{R })$$ has $$g-1...

14H05 | Real curve | Special type | Linear pencil | 14P99 | Mathematics, general | Teichmüller space | Mathematics | Separating gonality | 14H51 | MATHEMATICS | MATHEMATICS, APPLIED | REAL ALGEBRAIC-CURVES | Teichmuller space

14H05 | Real curve | Special type | Linear pencil | 14P99 | Mathematics, general | Teichmüller space | Mathematics | Separating gonality | 14H51 | MATHEMATICS | MATHEMATICS, APPLIED | REAL ALGEBRAIC-CURVES | Teichmuller space

Journal Article

Foundations of Computational Mathematics, ISSN 1615-3375, 4/2018, Volume 18, Issue 2, pp. 509 - 536

We prove that every bounded rational space curve of degree d and circularity c can be drawn by a linkage with $$ \frac{9}{2} d-6c+1$$ 92d-6c+1 revolute joints...

Secondary 13F20 | Linkage | Motion polynomial | Bennett flip | Linear and Multilinear Algebras, Matrix Theory | 68U07 | Mathematics | Factorization | Primary 70B05 | Numerical Analysis | 65D17 | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Dual quaternion | MATHEMATICS | MATHEMATICS, APPLIED | LINKAGES | COMPUTER SCIENCE, THEORY & METHODS | Theorems (Mathematics) | Curves, Algebraic | Polynomials | Research | Mathematical research

Secondary 13F20 | Linkage | Motion polynomial | Bennett flip | Linear and Multilinear Algebras, Matrix Theory | 68U07 | Mathematics | Factorization | Primary 70B05 | Numerical Analysis | 65D17 | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Economics, general | Dual quaternion | MATHEMATICS | MATHEMATICS, APPLIED | LINKAGES | COMPUTER SCIENCE, THEORY & METHODS | Theorems (Mathematics) | Curves, Algebraic | Polynomials | Research | Mathematical research

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 05/2018, Volume 86, pp. 189 - 214

We consider the parameterization f=(f0:f1:f2) of a plane rational curve C of degree n, and we study the singularities of C via such parameterization...

Rational curves | Projections | Parameterizations | Algorithms | Singularities | MATHEMATICS, APPLIED | SYZYGIES | COMPUTER SCIENCE, THEORY & METHODS | Analysis

Rational curves | Projections | Parameterizations | Algorithms | Singularities | MATHEMATICS, APPLIED | SYZYGIES | COMPUTER SCIENCE, THEORY & METHODS | Analysis

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 16, pp. 3189 - 3240

Let X be a curve of genus g >= 2 over a number field F of degree d = [F : Q]. The conjectural existence of a uniform bound N(g, d) on the number #X(F...

MATHEMATICS | REDUCTION | CHABAUTY | GEOMETRY

MATHEMATICS | REDUCTION | CHABAUTY | GEOMETRY

Journal Article

Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 6/2013, Volume 110, Issue 24, pp. 9669 - 9673

Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k...

Maps | Mathematical theorems | Topological theorems | Homeomorphism | Mathematical functions | Dynamical systems | Number theory | Jacobians | Curves | CONNES TYPE SYSTEMS | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Physical Phenomena | Algorithms | Finite fields | Research | Functions, Zeta | Physical Sciences

Maps | Mathematical theorems | Topological theorems | Homeomorphism | Mathematical functions | Dynamical systems | Number theory | Jacobians | Curves | CONNES TYPE SYSTEMS | MULTIDISCIPLINARY SCIENCES | Models, Theoretical | Physical Phenomena | Algorithms | Finite fields | Research | Functions, Zeta | Physical Sciences

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 12/2016, Volume 31, Issue 35, p. 1650188

.... We discuss the special case of moduli spaces of elliptic curves in detail. There, the Bagger–Witten line bundle does not exist as an ordinary line bundle, but rather is necessarily fractional...

moduli spaces | superconformal field theory | Bagger-Witten line bundle | STRING COMPACTIFICATIONS | SUPERGRAVITY | ILIOPOULOS D-TERMS | PHYSICS, NUCLEAR | WORLDSHEET INSTANTONS | QUANTIZATION | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

moduli spaces | superconformal field theory | Bagger-Witten line bundle | STRING COMPACTIFICATIONS | SUPERGRAVITY | ILIOPOULOS D-TERMS | PHYSICS, NUCLEAR | WORLDSHEET INSTANTONS | QUANTIZATION | MIRROR SYMMETRY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 1, pp. 711 - 722

...). The envelope of the family of lines {ℓλ}λ∈∂D is called the interior curve associated with B. In 2002, Daepp, Gorkin, and Mortini proved the interior curve associated with a Blaschke product of degree 3 forms an ellipse. While let Lλ...

Blaschke product | Dual curve | Algebraic curve | Complex analysis | ELLIPSES | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | MATRICES | Mathematics - Complex Variables

Blaschke product | Dual curve | Algebraic curve | Complex analysis | ELLIPSES | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | MATRICES | Mathematics - Complex Variables

Journal Article

The journal of high energy physics, ISSN 1029-8479, 2018, Volume 2018, Issue 5, pp. 1 - 7

...Published for SISSA by Springer Received: March 21, 2018 Accepted: April 23, 2018 Published: May 4, 2018 Conformal eld theories and compact curves in moduli...

Anomalies in Field and String Theories | Conformal Field Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Riemann surfaces | Mathematics - Algebraic Geometry | Nuclear and particle physics. Atomic energy. Radioactivity | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Anomalies in Field and String Theories | Conformal Field Theory | Quantum Physics | Differential and Algebraic Geometry | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, PARTICLES & FIELDS | Supersymmetry | Riemann surfaces | Mathematics - Algebraic Geometry | Nuclear and particle physics. Atomic energy. Radioactivity | Algebraic Geometry | Mathematics | High Energy Physics - Theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 10/2010, Volume 43, Issue 43, p. 434009

.... By giving a homology basis well adapted to the symmetries of Klein's curve, presented as a plane curve, we derive a new expression for its period matrix...

HYPERELLIPTIC CURVES | PERIOD MATRICES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SURFACES

HYPERELLIPTIC CURVES | PERIOD MATRICES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | SURFACES

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 109, Issue 2, pp. 423 - 447

A recent generalization of the “Kleinian sigma function” involves the choice of a point P of a Riemann surface X, namely a “pointed curve” (X, P...

Geometry | Primary 14K25 | Sigma function | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 14H40 | 14H50 | Physics | Trigonal cyclic cuve | Weierstrass semigroup | Secondary 14H55 | JACOBI INVERSION | STRATA | PHYSICS, MATHEMATICAL | Y(R)

Geometry | Primary 14K25 | Sigma function | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | 14H40 | 14H50 | Physics | Trigonal cyclic cuve | Weierstrass semigroup | Secondary 14H55 | JACOBI INVERSION | STRATA | PHYSICS, MATHEMATICAL | Y(R)

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2014, Volume 104, Issue 6, pp. 635 - 671

...) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle...

topological recursion | Secondary 34E20 | Higgs field | Theoretical, Mathematical and Computational Physics | Primary 14H15 | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 81T45 | Hitchin fibration | WKB approximation | 14H60 | 14H81 | Group Theory and Generalizations | family of spectral curves | quantum curve | HURWITZ NUMBERS | EQUATIONS | PHYSICS, MATHEMATICAL | MODULI SPACES | RECURSION | DUALITY | SPECTRAL CURVES | INTERSECTION THEORY | WEIL-PETERSSON VOLUMES | Sects

topological recursion | Secondary 34E20 | Higgs field | Theoretical, Mathematical and Computational Physics | Primary 14H15 | Statistical Physics, Dynamical Systems and Complexity | Physics | Geometry | 81T45 | Hitchin fibration | WKB approximation | 14H60 | 14H81 | Group Theory and Generalizations | family of spectral curves | quantum curve | HURWITZ NUMBERS | EQUATIONS | PHYSICS, MATHEMATICAL | MODULI SPACES | RECURSION | DUALITY | SPECTRAL CURVES | INTERSECTION THEORY | WEIL-PETERSSON VOLUMES | Sects

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 03/2019, Volume 21, Issue 2, p. 1850009

We study Shimura curves of PEL type in A g generically contained in the Prym locus...

Shimura varieties | Prym locus | Prym varieties | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | 2ND GAUSSIAN MAP | VARIETIES | MODULI SPACE | GENERIC TORELLI THEOREM

Shimura varieties | Prym locus | Prym varieties | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | 2ND GAUSSIAN MAP | VARIETIES | MODULI SPACE | GENERIC TORELLI THEOREM

Journal Article

Manuscripta mathematica, ISSN 1432-1785, 2018, Volume 160, Issue 3-4, pp. 315 - 325

Given a smooth curve $$\gamma $$ γ in some m-dimensional surface M in $$\mathbb {R}^{m+1}$$ R m + 1 , we study existence and uniqueness of a flat surface H having the same field of normal vectors as M along...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53B20 (secondary) | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53A07 (primary) | MATHEMATICS | DEVELOPABLE SURFACES

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53B20 (secondary) | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53A07 (primary) | MATHEMATICS | DEVELOPABLE SURFACES

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 12/2017, Volume 28, Issue 13, p. 1750099

We study the deformations of a smooth curve C on a smooth projective 3 -fold V , assuming the presence of a smooth surface S satisfying C ⊂ S ⊂ V...

K3 surface | Fano threefold | Hilbert scheme | Obstruction | Infinitesimal deformation | MATHEMATICS | obstruction | NON-REDUCED COMPONENTS | SPACE-CURVES | ALGEBRAIC-GEOMETRY | infinitesimal deformation | CONE | Mathematics - Algebraic Geometry

K3 surface | Fano threefold | Hilbert scheme | Obstruction | Infinitesimal deformation | MATHEMATICS | obstruction | NON-REDUCED COMPONENTS | SPACE-CURVES | ALGEBRAIC-GEOMETRY | infinitesimal deformation | CONE | Mathematics - Algebraic Geometry

Journal Article

2001, London Mathematical Society lecture note series, ISBN 9780521665438, Volume 288, x, 245

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists...

Coding theory | Curves, Algebraic | Finite fields (Algebra)

Coding theory | Curves, Algebraic | Finite fields (Algebra)

Book

Geometriae Dedicata, ISSN 0046-5755, 8/2018, Volume 195, Issue 1, pp. 193 - 201

Let $$f: S\longrightarrow B$$ f:S⟶B be a non-trivial fibration from a complex projective smooth surface S to a smooth curve B of genus b. Let $$c_f...

Plane curves | Mathematics | Topology | 14H50 | Relative irregularity | 14D06 | 14J99 | Jacobian ideals | Xiao’s conjecture | 14B10 | Convex and Discrete Geometry | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Differential Geometry | MATHEMATICS | Xiao's conjecture | Mathematics - Algebraic Geometry | Corbes planes

Plane curves | Mathematics | Topology | 14H50 | Relative irregularity | 14D06 | 14J99 | Jacobian ideals | Xiao’s conjecture | 14B10 | Convex and Discrete Geometry | Algebraic Geometry | Hyperbolic Geometry | Projective Geometry | Differential Geometry | MATHEMATICS | Xiao's conjecture | Mathematics - Algebraic Geometry | Corbes planes

Journal Article

PloS one, ISSN 1932-6203, 2019, Volume 14, Issue 1, p. e0208015

An imperative curve modeling technique has been established with a view to its applications in various disciplines of science, engineering and design...

MULTIDISCIPLINARY SCIENCES | Comparative analysis | Trigonometrical functions | Research | Computers | Design engineering | Engineering | Applied mathematics | Computer aided design--CAD | Computer graphics | International conferences | Modelling | Polynomials | Trigonometric functions | Smoothness | CAD | Computer aided design

MULTIDISCIPLINARY SCIENCES | Comparative analysis | Trigonometrical functions | Research | Computers | Design engineering | Engineering | Applied mathematics | Computer aided design--CAD | Computer graphics | International conferences | Modelling | Polynomials | Trigonometric functions | Smoothness | CAD | Computer aided design

Journal Article

Electronics Letters, ISSN 0013-5194, 9/2015, Volume 51, Issue 18, pp. 1466 - 1468

A system that achieves compression using artificial DNA packaging with the support of two algebraic curves is presented, whereby the Hermitian channel code algorithm introduces gain and safety...

Wireless communications | telecommunication security | secure DNA data compression | data compression | uncoded quadrature phase shift keying | channel coding | artificial DNA packaging | algebraic curve | Hermitian matrices | BER | ENGINEERING, ELECTRICAL & ELECTRONIC | CODES | CHANNEL | wireless channels | Hermitian channel code algorithm | error statistics | Noise levels | Algebra | Compressing | Deoxyribonucleic acid | Data compression | Packaging | Channels | Gain

Wireless communications | telecommunication security | secure DNA data compression | data compression | uncoded quadrature phase shift keying | channel coding | artificial DNA packaging | algebraic curve | Hermitian matrices | BER | ENGINEERING, ELECTRICAL & ELECTRONIC | CODES | CHANNEL | wireless channels | Hermitian channel code algorithm | error statistics | Noise levels | Algebra | Compressing | Deoxyribonucleic acid | Data compression | Packaging | Channels | Gain

Journal Article