Geometric Invariant Theory for Polarized Curves

Bini, Gilberto; Felici, Fabio; Melo, Margarida; Viviani, Filippo

doi:10.1007/978-3-319-11337-1

Cited by 6 publications

(6 citation statements)

References 28 publications

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“…When n = 0, as explained in [KP19, Remark 5.14], the stack J g,0 (φ can ) is isomorphic to Caporaso's universal compactified Jacobian [Cap94,Cap08], which is studied in detail in [Mel09], [BFV12], [BMV12], [MV14], [BMV12], [BFMV14], [CMKV15], [CMKV17] and is, in turn, isomorphic to Pandharipande's universal compactified Jacobian [Pan96] (see [EP16]). Note that in this case φ can is general precisely when d − g + 1 and 2g − 2 are coprime (see [Cap94,Proposition 6.2] and [KP19, Remark 5.12]).…”

Section: Canonical Stability Condition and Break Divisorsmentioning

confidence: 99%

Tropicalization of the universal Jacobian

Melo¹,

Molcho²,

Ulirsch³

et al. 2022

Épijournal De Géométrie Algébrique

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In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.

show abstract

Section: Canonical Stability Condition and Break Divisorsmentioning

confidence: 99%

Tropicalization of the universal Jacobian

Melo¹,

Molcho²,

Ulirsch³

et al. 2022

Épijournal De Géométrie Algébrique

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Canonical Stability Condition and Break Divisorsmentioning

confidence: 99%

Tropicalization of the universal Jacobian

Melo¹,

Molcho²,

Ulirsch³

et al. 2021

Preprint

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A. In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.

show abstract

“…In other words, the goal is to construct compactifications of the universal moduli space of semistable vector bundles over each step of the minimal model program for M g . In the rank one case, the conjectural first two steps of the LMMP for the Caporaso's compactification J d,g have been described by Bini-Felici-Melo-Viviani in [6]. From the stacky point of view, the first step (resp.…”

Section: Introductionmentioning

confidence: 99%

“…The boundary divisors which are not extremal will be called non-extremal boundary divisors (for a precise description see §2. 6). By smoothness of Vec r,d,g , the divisors { δ j i } give us line bundles.…”

Section: Introductionmentioning

confidence: 99%