Twisted Bundles and Admissible Covers

Abramovich, Dan; Corti, Alessio; Vistoli, Angelo

doi:10.1081/agb-120022434

Cited by 264 publications

(624 citation statements)

References 16 publications

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“…Initially the theory was focused on the case ℓ = 2 of Prym curves, for which A. Beauville put forward the theory of admissible covers ( [Bea77] and [ACV03]). It extends the modular description of points in R g,2 as étale double covers C ′ → C to stable curves.…”

Section: Modular Compactificationmentioning

confidence: 99%

Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline {\mathcal {M}}_{8}$

Bruns

2018

Trans. Amer. Math. Soc.

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Twists of Mukai bundles and the geometry of the level 3 modular variety over M 8 Gregor Bruns AbstractFor a curve C of genus 6 or 8 and a torsion bundle η of order ℓ we study the vanishing of the space of global sections of the twist E C ⊗ η of the rank two Mukai bundle E C of C. The bundle E C was used in a well-known construction of Mukai which exhibits general canonical curves of low genus as sections of Grassmannians in the Plücker embedding.Globalizing the vanishing condition, we obtain divisors on the moduli spaces R 6,ℓ and R 8,ℓ of pairs [C, η]. First we characterize these divisors by different conditions on linear series on the level curves, afterwards we calculate the divisor classes. As an application, we are able to prove that R 8,3 is of general type.

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Section: Modular Compactificationmentioning

confidence: 99%

Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline {\mathcal {M}}_{8}$

Bruns

2018

Trans. Amer. Math. Soc.

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“…Recall that the notion of rigidification of a Deligne-Mumford stack is a process to get rid of given stabilizers in a "minimal" manner; see [ACV,Section 5.1]. Throughout this paper, we fix the following definition of rigidification.…”

Section: Rigidificationmentioning

confidence: 99%

Unitary representations of the fundamental group of orbifolds

Biswas

Hogadi

2016

Proc Math Sci

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“…, and extend by scalars to obtained (1). One checks that the product rule for exponentials implies that this lift preserves the compatibility with the algebra structure.…”

Section: We Next Havementioning

confidence: 99%

Mochizuki’s Crys-Stable Bundles: A Lexicon and Applications

Osserman

2007

Publ. Res. Inst. Math. Sci.

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Mochizuki's work on torally crys-stable bundles [18] has extensive implications for the theory of logarithmic connections on vector bundles of rank 2 on curves, once the language is translated appropriately. We describe how to carry out this translation, and give two classes of applications: first, one can conclude almost immediately certain results classifying Frobenius-unstable vector bundles on curves; and second, it follows from the results of [22] that one also obtains results on rational functions with prescribed ramification in positive characteristic. §1. IntroductionMochizuki's theory of torally crys-stable bundles and torally indigenous bundles developed in [18] has, after appropriate translation, immediate implications for logarithmic connections on vector bundles of rank 2 on curves. This in turn has immediate implications to a subject which has recently been studied by a number of different people (see, for instance,

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Twisted Bundles and Admissible Covers

Cited by 264 publications

References 16 publications

Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline {\mathcal {M}}_{8}$

Twists of Mukai bundles and the geometry of the level $3$ modular variety over $\overline {\mathcal {M}}_{8}$

Unitary representations of the fundamental group of orbifolds

Mochizuki’s Crys-Stable Bundles: A Lexicon and Applications

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