Wronski algebra systems on families of singular curves

Esteves, Eduardo

doi:10.24033/asens.1736

Cited by 14 publications

(12 citation statements)

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“…Now, R F (V ) might be infinite, indeed: Proposition 2.5. ( [4], Prop. 7.8, p. 133) The ramification scheme R F (V ) is finite if and only if F is square-free and the linear system V is nondegenerate on each geometric irreducible component of C.…”

Section: Wronskians and Ramification Schemesmentioning

confidence: 99%

Limits of dual curves via foliations

Esteves¹,

Medeiros²,

Sousa³

2019

Preprint

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Section: Wronskians and Ramification Schemesmentioning

confidence: 99%

Limits of dual curves via foliations

Esteves¹,

Medeiros²,

Sousa³

2019

Preprint

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“…Again, it is not shown in [11] that γ restricts to the fundamental class on each geometric fiber. This can be derived from the fact that the construction given to γ commutes with base change, and from [34], Cor.…”

Section: 2mentioning

confidence: 99%

“…4.36, p. 89 should imply this, at least if the geometric fibers of π are irreducible. Also, if the geometric fibers of C/S are locally complete intersections, then the existence of a map γ : Ω 1 C/S → ω C/S was pointed out in [11].…”

Section: 2mentioning

confidence: 99%

Generalized Linear Systems on Curves and Their Weierstrass Points

Esteves¹,

Nogueira²

2013

Communications in Algebra

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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 .

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“…cit., reviewed in Section 2, was to consider a general family of smooth curves, a natural map of vector bundles over its total space whose top degeneracy scheme parameterizes the Weierstrass points of hyperelliptic fibers of π, apply Porteous Formula to compute the class of this scheme, and then compute the pushforward of this class to the base of the family. However, according to [7], p. 169, even though "trying to extend the application of Porteous' formula" to a general family of stable curves "is the most obvious approach" to obtaining a formula for [H], the problem is that a certain bundle of jets, namely (2), defined on the smooth locus of the family, "cannot be extended to a vector bundle over the nodes of fibers of the family of curves." This motivated their question, mentioned above.…”

Section: Introductionmentioning

confidence: 99%