Fine compactified Jacobians

Melo, Margarida; Viviani, Filippo

doi:10.1002/mana.201100021

Cited by 25 publications

(39 citation statements)

References 31 publications

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“…It would be interesting to know if these isomorphisms extend to the compactifications. Important results along these lines can be found in [Melo and Viviani 2012;Esteves 2009], but many basic question remain unanswered. Currently, there is no example of a curve X 0 → Spec(k) such that two Esteves compactified Jacobians associated to X 0 are nonisomorphic.…”

Section: Applicationsmentioning

confidence: 97%

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Two ways to degenerate the Jacobian are the same

Kass

2013

Algebra Number Theory

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Section: Applicationsmentioning

confidence: 97%

“…The space is constructed as a closed subspace of a (nonnoetherian, nonseparated) algebraic space that was constructed in [Altman and Kleiman 1980]. For nodal curves, Melo and Viviani [2012] describe the relation between the Esteves moduli spaces and the Simpson moduli spaces. However, here we treat these moduli spaces separately.…”

mentioning

confidence: 99%

Two ways to degenerate the Jacobian are the same

Kass

2013

Algebra Number Theory

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“…Notice that this last property implies that stability and semistability coincide and therefore that Simpson's compactified Jacobian is also a fine moduli space in this case. In the special case when the family f has only nodal singularities, the previous result was known by work of the author together with Viviani in [MV12]. In loc.…”

Section: Line Bundles Loci In Compactifiedmentioning

confidence: 77%

Universal Néron models for Jacobians of curves with marked points

Melo

2016

Boll Unione Mat Ital

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We consider the problem of constructing universal Néron models for families of curves with sections. By applying a construction of the author of universal compactified Jacobians over the moduli stack of reduced curves with markings and a result by J. Kass, we get a positive answer for smooth families of curves with planar singularities over Dedekind schemes.Question 1.1. Let M g,n be the moduli stack of reduced curves of given genus g and with n distinct markings. Is there a modular algebraic stack N g,n endowed with a map onto M g,n such that N g,n is a universal Néron model for the Jacobians of families of curves in M g,n ? Moreover, can we describe a modular compactification of N g,n over M g,n ?By a universal Néron model we mean an algebraic stack N g,n endowed with a map π onto M g,n such that given a family of curves (f : X → B; σ 1 , . . . , σ n ) ∈ M g,n (B) over a Dedekind scheme B, which is smooth over a dense open subset U ⊆ B, the pullback of N g,n → M g,n via the moduli map of the family µ f : B → M g,n is isomorphic to the Néron model of J(X U ) over B:A different possibility for extending J(X U ) over B is to take a compactified Jacobian of the family f . This is a proper model of J(X U ) → U and in the case when f has non-integral 1991 Mathematics Subject Classification. Primary 14H10; Secondary 14H40.

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“…The following result, due to Busonero, Kass and Melo‐Viviani, states a relationship between

J_{E}^{σ}

and

N (J_{C_{K}})

. Theorem The B ‐smooth locus of

J_{E}^{σ}

is isomorphic to the Néron model of

J_{{scriptC}_{K}}

. Proof See [, , Theorem A] and [, Theorem 3.1].

□

…”

Section: Extending Abel Mapsmentioning

confidence: 99%

“…A recent result (see [4], [21], [23]) shows that the Néron model of the Jacobian variety of the generic fiber of f is isomorphic to the B-smooth locus of J σ E . This is as an extension of a previous result of Caporaso (see [7]).…”

Section: Introductionmentioning

confidence: 99%

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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Fine compactified Jacobians

Cited by 25 publications

References 31 publications

Two ways to degenerate the Jacobian are the same

Two ways to degenerate the Jacobian are the same

Universal Néron models for Jacobians of curves with marked points

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

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