Limit canonical systems on curves with two components

Esteves, Eduardo; Medeiros, Nivaldo

doi:10.1007/s002220200211

Cited by 33 publications

(82 citation statements)

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“…,N t on C to form an enriched structure were found in [7], Prop. 3.16; see also [6], Thm. 6.10, p. 297.…”

Section: Introductionmentioning

confidence: 90%

“…Then h 1 (C I , K β I ) = 1, and thus h 1 (C I , K β I (P )) ≤ 1 with equality only if P = 0. However, from the expression (6), and the hypothesis that δ i,j = 0 for all i and j, we see that P = 0 only if n j ≤ n i for all i ∈ I and j ∈ I, and hence only if γ…”

Section: If For Each I ∈ I the Restriction Mapmentioning

confidence: 98%

“…Since the smoothing occurs along a general direction, it follows from [6], Cor. 6.9, p. 297 that L n f is the general invertible sheaf whose restriction to C J is isomorphic to L J for each n-balanced J ⊆ {1, .…”

Section: If For Each I ∈ I the Restriction Mapmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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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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“…,N t on C to form an enriched structure were found in [7], Prop. 3.16; see also [6], Thm. 6.10, p. 297.…”

Section: Introductionmentioning

confidence: 90%

Section: If For Each I ∈ I the Restriction Mapmentioning

confidence: 98%

Section: If For Each I ∈ I the Restriction Mapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Limit Weierstrass points on nodal reducible curves

Esteves

Salehyan

2007

Trans. Amer. Math. Soc.

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The resolution of the degree‐2 Abel‐Jacobi map for nodal curves‐I

Pacini

2014

Mathematische Nachrichten

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Let f:C→B be a regular local smoothing of a nodal curve. In this paper, we find a modular description of the Néron maps associated to Abel‐Jacobi maps with values in Esteves's fine compactified Jacobian and with source the B‐smooth locus of either the double product of scriptC over B or the degree‐2 Hilbert scheme of the family f. This is the first of a series of two papers dedicated to the construction of a resolution of the degree‐2 Abel‐Jacobi map for a regular smoothing of a nodal curve.

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Linear series on metrized complexes of algebraic curves

2014

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Abstract. A metrized complex of algebraic curves over an algebraically closed field κ is, roughly speaking, a finite metric graph Γ together with a collection of marked complete nonsingular algebraic curves Cv over κ, one for each vertex v of Γ; the marked points on Cv are in bijection with the edges of Γ incident to v. We define linear equivalence of divisors and establish a Riemann-Roch theorem for metrized complexes of curves which combines the classical Riemann-Roch theorem over κ with its graph-theoretic and tropical analogues from [AC, BN, GK, MZ], providing a common generalization of all of these results. For a complete nonsingular curve X defined over a non-Archimedean field K, together with a strongly semistable model X for X over the valuation ring R of K, we define a corresponding metrized complex CX of curves over the residue field κ of K and a canonical specialization map τ CX * from divisors on X to divisors on CX which preserves degrees and linear equivalence. We then establish generalizations of the specialization lemma from [B] and its weighted graph analogue from [AC], showing that the rank of a divisor cannot go down under specialization from X to CX. As an application, we establish a concrete link between specialization of divisors from curves to metrized complexes and the Eisenbud-Harris theory [EH] of limit linear series. Using this link, we formulate a generalization of the notion of limit linear series to curves which are not necessarily of compact type and prove, among other things, that any degeneration of a g r d in a regular family of semistable curves is a limit g r d on the special fiber.

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Limit canonical systems on curves with two components

Cited by 33 publications

References 10 publications

Limit Weierstrass points on nodal reducible curves

Limit Weierstrass points on nodal reducible curves

The resolution of the degree‐2 Abel‐Jacobi map for nodal curves‐I

Linear series on metrized complexes of algebraic curves

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