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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
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
Journal Article
Foundations of Computational Mathematics, ISSN 1615-3375, 4/2018, Volume 18, Issue 2, pp. 509 - 536
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
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
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 0027-8424, 6/2013, Volume 110, Issue 24, pp. 9669 - 9673
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
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
Journal Article
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
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)
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
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
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}$$ R m + 1 , we study existence and uniqueness of a flat surface H having the same field of normal vectors as M along... 
Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53B20 (secondary) | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 53A07 (primary) | MATHEMATICS | DEVELOPABLE SURFACES
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 12/2017, Volume 28, Issue 13, p. 1750099
We study the deformations of a smooth curve C on a smooth projective 3 -fold V , assuming the presence of a smooth surface S satisfying C ⊂ S ⊂ V... 
K3 surface | Fano threefold | Hilbert scheme | Obstruction | Infinitesimal deformation | MATHEMATICS | obstruction | NON-REDUCED COMPONENTS | SPACE-CURVES | ALGEBRAIC-GEOMETRY | infinitesimal deformation | CONE | Mathematics - Algebraic Geometry
Journal Article
2001, London Mathematical Society lecture note series, ISBN 9780521665438, Volume 288, x, 245
Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists... 
Coding theory | Curves, Algebraic | Finite fields (Algebra)
Book
Geometriae Dedicata, ISSN 0046-5755, 8/2018, Volume 195, Issue 1, pp. 193 - 201
Let $$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
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
Journal Article
Electronics Letters, ISSN 0013-5194, 9/2015, Volume 51, Issue 18, pp. 1466 - 1468
Journal Article
2005, ISBN 9812564594, xi, 272
Book