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On the geometry of Deligne-Mumford stacks


Kresch, A (2009). On the geometry of Deligne-Mumford stacks. In: Abramovich, D; Bertram, A; Katzarkov, L; Pandharipande, R; Thaddeus, M. Algebraic Geometry: Seattle 2005. Providence, Rhode Island: American Mathematical Society, 259-271.

Abstract

General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi-)projective” Deligne–Mumford stacks is identified,
defined to be those that embed as a (locally) closed substack of a smooth proper Deligne–Mumford stack having projective coarse moduli space. These conditions are shown to be equivalent to some well-studied hypotheses.

Abstract

General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi-)projective” Deligne–Mumford stacks is identified,
defined to be those that embed as a (locally) closed substack of a smooth proper Deligne–Mumford stack having projective coarse moduli space. These conditions are shown to be equivalent to some well-studied hypotheses.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:16 Nov 2009 19:37
Last Modified:15 Apr 2021 14:01
Publisher:American Mathematical Society
Series Name:Proceedings of symposia in pure mathematics
Number:80,1
ISSN:0082-0717
ISBN:978-0-8218-4702-2
Additional Information:Algebraic Geometry, Seattle 2005 : 2005 Summer Research Institute, July 25-August 12, 2005, University of Washington, Seattle
OA Status:Green
Official URL:http://www.ams.org/bookstore-getitem/item=PSPUM-80-1

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