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Compactifying picard stacks over degenerations of surfaces

Author: Atoshi Chowdhury; Ravi Vakil; Eleny Ionel; Jun Li; Stanford University. Department of Mathematics.
Publisher: 2012.
Dissertation: Thesis (Ph. D.)--Stanford University, 2012.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
Moduli spaces of smooth varieties can be partially compactified by the addition of a boundary parametrizing reducible varieties. We address the question of partially compactifying the universal Picard stack (the moduli space of line bundles) over a moduli space of smooth varieties by extending it over such a partial compactification. We present a stability condition for line bundles on reducible varieties and use it  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Atoshi Chowdhury; Ravi Vakil; Eleny Ionel; Jun Li; Stanford University. Department of Mathematics.
OCLC Number: 795012989
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource.
Responsibility: Atoshi Chowdhury.

Abstract:

Moduli spaces of smooth varieties can be partially compactified by the addition of a boundary parametrizing reducible varieties. We address the question of partially compactifying the universal Picard stack (the moduli space of line bundles) over a moduli space of smooth varieties by extending it over such a partial compactification. We present a stability condition for line bundles on reducible varieties and use it to specify what boundary points should be added to the universal Picard stack to obtain a proper moduli space. Over surfaces with exactly two irreducible components, we give specific results on enumerating stable line bundles, which support the conjecture that these are the right boundary points to add. This generalizes work of Caporaso and others in the 1990s on compactifying the universal Picard variety over the moduli space of curves.

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