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Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 12/2016, Volume 26, Issue 8, pp. 1503 - 1528
For a given linear system on a curve, the number of divisors of a certain type contained in this system is known as the formula of de Jonquières... 
Families of nodal curves | relative Hilbert schemes | de Jonquières' formula | MATHEMATICS | de Jonquieres' formula
Journal Article
Boletim da Sociedade Brasileira de Matemática, ISSN 1678-7714, 2018, Volume 50, Issue 3, pp. 717 - 743
Let C be a nodal curve and L be an invertible sheaf on C. Let $$\alpha _{L}:C\dashrightarrow J_{C}$$ α L : C ⤏ J C be the degree-1 rational Abel map, which takes a smooth point... 
Mathematics, general | Nodal curves | Mathematics | 14H50 | Theoretical, Mathematical and Computational Physics | Abel map | MATHEMATICS | COMPACTIFICATION | Mathematics - Algebraic Geometry
Journal Article
Advances in Mathematics, ISSN 0001-8708, 09/2013, Volume 244, pp. 413 - 440
An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers... 
Nodal stable curves | Noded Riemann surfaces | Moduli cotangent bundle | Plumbing construction | Holomorphic quadratic differentials | MATHEMATICS | RIEMANN SURFACES | MODULI SPACE | CANONICAL METRICS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 348, Issue 1, pp. 315 - 335
Journal Article
Collectanea mathematica (Barcelona), ISSN 2038-4815, 2018, Volume 70, Issue 1, pp. 107 - 115
Let (S, L) be a polarized K3 surface with $$\mathrm {Pic}(S) = \mathbb {Z}[L]$$ Pic ( S ) = Z [ L ] and $$L\cdot L=2g-2$$ L · L = 2 g - 2 , let C be a nonsingular curve of genus... 
Geometry | K3 surface | Secondary 14H51 | Algebra | Gaussian map | Primary 14J28 | Nodal curve | Analysis | Wahl map | Mathematics | Applications of Mathematics | 14H10 | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR SERIES
Journal Article
Collectanea Mathematica, ISSN 0010-0757, 9/2016, Volume 67, Issue 3, pp. 533 - 538
A theorem of Green says that a line bundle of degree $${\ge }2g+1+p$$ ≥ 2 g + 1 + p on a smooth curve X of genus g has property $$\mathrm N_p$$ N p... 
Geometry | Linear systems | 14N99 | Nodal curves | Algebra | Analysis | Property $$\hbox {N}_p$$ N p | Syzygies | Mathematics | Applications of Mathematics | 14H99 | Property N | MATHEMATICS | MATHEMATICS, APPLIED | Property N-p
Journal Article
Arkiv för Matematik, ISSN 0004-2080, 4/2016, Volume 54, Issue 1, pp. 55 - 83
Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain... 
Mathematics, general | Mathematics | MATHEMATICS | STABLE CURVES | BUNDLES | MODULI STACK | NODAL CURVES | (M)OVER-BAR(G) | PICARD SCHEME | SHEAVES | Family | Mathematics - Algebraic Geometry
Journal Article
Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica, ISSN 0365-1029, 01/2014, Volume 68, Issue 1, p. 11
  Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality s[r](C... 
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2012, Volume 270, Issue 3, pp. 871 - 887
...) consisting of a general projective K3 surface S, and a curve C obtained as the normalization of a nodal, hyperplane section $${\hat C\hookrightarrow... 
Nodal curves | Deformations | Wahl map | 14J28 | Mathematics, general | Mathematics | K 3 surfaces | 14D15 | 14H10 | K3 surfaces | GAUSSIAN MAPS | MATHEMATICS
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 11/2007, Volume 18, Issue 10, pp. 1133 - 1150
We study the Brill–Noether loci for semistable torsionfree sheaves of small slopes on a nodal curve... 
Brill-Noether theory | Vector bundles | Nodal curves | MATHEMATICS | SMALL SLOPES | STABLE VECTOR-BUNDLES | vector bundles | TORSION-FREE SHEAVES | MODULI SPACES | nodal curves
Journal Article
The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, 7/2010, Volume 49, Issue 5, pp. 663 - 674
Journal Article
The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, 2/2014, Volume 70, Issue 5, pp. 995 - 1007
Journal Article
Asian Journal of Mathematics, ISSN 1093-6106, 2013, Volume 17, Issue 2, pp. 193 - 264
...) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called 'tautological module', generated by diagonal loci, node scrolls, and twists thereof... 
Nodal curves | Intersection theory | Hilbert scheme | Enumerative geometry | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | enumerative geometry | intersection theory | nodal curves | 14N99 | 14H99
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 09/2017, Volume 94, Issue 9, pp. 1879 - 1889
In this work, we present a use of nodal curves to detect the compositeness of a given odd integer... 
generalized Jacobian | Nodal curves | primality test | 68W20 | STRONG PSEUDOPRIMES | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | BASES | 11G20 | 11G99 | 11Y11 | 11Y16 | PRIMALITY | Algorithms
Journal Article
Communications in Algebra, ISSN 0092-7872, 02/2014, Volume 42, Issue 2, pp. 755 - 763
In this article, we consider the tautological ring containing the extended Brill-Noether algebraic classes on the normalization of the compactified Jacobian of a complex nodal projective curve (with one node). This smallest ℚ... 
Nodal curve | Chow groups | Parabolic line bundles | MATHEMATICS | NODAL CURVES | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2018, Volume 333, pp. 670 - 693
.... We show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on K3 and del Pezzo surfaces respectively... 
Strata of differentials | Unirational | Uniruled | Moduli of curves | Quadratic differentials | MATHEMATICS | EFFECTIVE DIVISORS | SEVERI VARIETIES | K3 SURFACES | DEFORMATIONS | NODAL CURVES | MODULI SPACES
Journal Article
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2019, Volume 15
This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and L-twisted Hitchin pairs on nodal curves... 
Higgs bundles | REPRESENTATIONS | FUNDAMENTAL GROUP | generalised parabolic structures | GENERALIZED PARABOLIC BUNDLES | PHYSICS, MATHEMATICAL | MODULI | nodal curves | VECTOR-BUNDLES
Journal Article
Kyushu journal of mathematics, ISSN 1340-6116, 2014, Volume 68, Issue 1, pp. 139 - 147
We study Weierstrass points on a smooth curve C whose first two non-gaps equal n and n + 2... 
algebraic curves | Weierstrass points | Algebraic curves | MATHEMATICS | NODAL CURVES
Journal Article
ARCHIV DER MATHEMATIK, ISSN 0003-889X, 02/2020, Volume 114, Issue 2, pp. 171 - 174
...)-spanned line bundle, then the equigeneric Severi variety V-g(L) of all curves in vertical bar L vertical bar having genus g is non-empty, irreducible, of the expected... 
MATHEMATICS | Nodal curves | Enriques surfaces | ORDER EMBEDDINGS | K3 | PROOF | RATIONAL CURVES | Abelian surfaces | K3 surfaces | Severi variety
Journal Article
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