Weierstrass Weight and Degenerations

Lax, R. F.

doi:10.2307/2046542

Cited by 3 publications

(3 citation statements)

References 3 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, singular points of irreducible curves, at least those with Gorenstein singularities, are always limits of Weierstrass points. Major work was done by Widland, Lax and Garcia ( [18], [31], [32], [33], [41]) in the 1980's and early 1990's to define and study Weierstrass points of linear systems on such curves. In particular, Lax showed that these Weierstrass points are the limits of the Weierstrass points of linear systems on smooth curves degenerating to the given linear system on the singular curve; see [32], Prop.…”

Section: Introductionmentioning

confidence: 99%

Generalized Linear Systems on Curves and Their Weierstrass Points

Esteves¹,

Nogueira²

2013

Communications in Algebra

View full text Add to dashboard Cite

Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I, ǫ) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces ǫ : V → Γ(C, I). If the system is nondegenerate on every irreducible component of C, we associate to it a 0-cycle W , its Weierstrass cycle. Then we show that for each one-parameter family of curves C t degenerating to C, and each family of linear systems (L t , ǫ t ) along C t , with L t invertible, degenerating to (I, ǫ), the corresponding Weierstrass divisors degenerate to a subscheme whose associated 0-cycle is W . We show that the limit subscheme contains always an "intrinsic" subscheme, canonically associated to (I, ǫ), but the limit itself depends on the family L t .

show abstract

Section: Introductionmentioning

confidence: 99%

Generalized Linear Systems on Curves and Their Weierstrass Points

Esteves¹,

Nogueira²

2013

Communications in Algebra

View full text Add to dashboard Cite

show abstract

“…Second, we are able to consider families of singular curves in any characteristic, instead of a single curve as in the previous literature (see however [13] in characteristic 0). In [10] Laksov and Thorup independently introduce substitutes for the sheaves of principal parts on an integral, Gorenstein curve.…”

Section: Introductionmentioning

confidence: 99%

Wronski algebra systems on families of singular curves

Esteves¹

1996

Ann. Sci. École Norm. Sup.

View full text Add to dashboard Cite

Wronski algebra systems on families of singular curves Annales scientifiques de l'É.N.S. 4 e série, tome 29, n o 1 (1996), p. 107-134 © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1996, tous droits réservés. L'accès aux archives de la revue « Annales scientifiques de l'É.N.S. » (http://www. elsevier.com/locate/ansens) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

show abstract

“…Weierstrass points on integral Gorenstein curves were defined in [13] using the (canonical) line bundle of dualizing differentials. The limit Weierstrass points on such a fiber in a family are these intrinsically defined Weierstrass points by [9]. Put…”

mentioning

confidence: 99%

Limit Weierstrass Points on the Kenyon-Smillie Family of Plane Quartics

Lax

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Costantini and Kappes gave an algebraic equation of the universal family over the Kenyon-Smillie (2,3,4)-Teichmüller curve. This equation gives rise to a family of projective plane quartic curves with three singular members. These singular curves are: (1) an integral nodal quartic, (2) the union of a line and a nodal cubic, and (3) a quadruple line. We determine the limit Weierstrass points on these singular curves.

show abstract

Weierstrass Weight and Degenerations

Abstract: ABSTRACT. It is shown that as a family of projective smooth curves degenerates to an irreducible Gorenstein curve the Weierstrass weight at a point P on the limit curve is the sum of the Weierstrass weights at points on the smooth curves converging to P.

Cited by 3 publications

References 3 publications

Generalized Linear Systems on Curves and Their Weierstrass Points

Generalized Linear Systems on Curves and Their Weierstrass Points

Wronski algebra systems on families of singular curves

Limit Weierstrass Points on the Kenyon-Smillie Family of Plane Quartics

Contact Info

Product

Resources

About