Limits of Weierstrass points in regular smoothings of curves with two components

Esteves, Eduardo; Medeiros, Nivaldo

doi:10.1016/s0764-4442(00)00294-9

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Introduction2

Limiting Behavior Of Weierstrass Points In Degenerating Fami1

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2002

2016

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Cited by 3 publications

(3 citation statements)

References 2 publications

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“…This subject, which was previously studied by Eisenbud-Harris [EH87], EstevesMedeiros [EM00], and several other authors, has seen important recent advances by Amini [Ami14]. We now summarize the main results proved in Amini's paper.…”

Section: Limiting Behavior Of Weierstrass Points In Degenerating Famimentioning

confidence: 76%

Degeneration of Linear Series from the Tropical Point of View and Applications

Baker

Jensen

2016

Simons Symposia

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Section: Limiting Behavior Of Weierstrass Points In Degenerating Famimentioning

confidence: 76%

Degeneration of Linear Series from the Tropical Point of View and Applications

Baker

Jensen

2016

Simons Symposia

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“…In [5] and [6] limits of Weierstrass points on two-component curves are described in detail. In [5] smoothings along general directions (for which the total space of the smoothing is regular) were studied, whereas in [6] all smoothings were considered.…”

Section: Introductionmentioning

confidence: 99%

“…In [5] smoothings along general directions (for which the total space of the smoothing is regular) were studied, whereas in [6] all smoothings were considered. The present article is thus a generalization of [5]. It might be possible, and interesting, to pursue our study further, and consider all smoothings of a given curve.…”

Section: Introductionmentioning

confidence: 99%

Limit Weierstrass points on nodal reducible curves

Esteves

Salehyan

2007

Trans. Amer. Math. Soc.

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Abstract. In the 1980s D. Eisenbud and J. Harris posed the following question: "What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type?" In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

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Limit canonical systems on curves with two components

Esteves¹,

Medeiros²

2002

Inventiones Mathematicae

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Abstract. In the 80's D. Eisenbud and J. Harris considered the following problem: "What are the limits of Weierstrass points in families of curves degenerating to stable curves?" But for the case of stable curves of compact type, treated by them, this problem remained wide open since then. In the present article, we propose a concrete approach to this problem, and give a quite explicit solution for stable curves with just two irreducible components meeting at points in general position.

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Limits of Weierstrass points in regular smoothings of curves with two components

Cited by 3 publications

References 2 publications

Degeneration of Linear Series from the Tropical Point of View and Applications

Degeneration of Linear Series from the Tropical Point of View and Applications

Limit Weierstrass points on nodal reducible curves

Limit canonical systems on curves with two components

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