Volume 16, issue 4 (2012)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Virtual push-forwards

Cristina Manolache

Geometry & Topology 16 (2012) 2003–2036
Abstract

Let p: F G be a morphism of DM stacks of positive virtual relative dimension k and let γ Ak(F). We give sufficient conditions for p(γ [F]virt) to be a multiple of [G]virt. We show an analogue of the conservation of number for virtually smooth families. We show implications to Gromov–Witten invariants and give a new proof of a theorem of Marian, Oprea and Pandharipande which compares the virtual classes of moduli spaces of stable maps and moduli spaces of stable quotients.

Keywords
virtual classes, Gromov–Witten invariants
Mathematical Subject Classification 2010
Primary: 14C17
Secondary: 14N35
References
Publication
Received: 14 March 2012
Accepted: 6 May 2012
Published: 31 August 2012
Proposed: Richard Thomas
Seconded: Jim Bryan, Simon Donaldson
Authors
Cristina Manolache
Institut für Mathematik
Humboldt-Universität zu Berlin
Unter den Linden 6
10099 Berlin
Germany