Virtual push-forwards

Manolache, Cristina

doi:10.2140/gt.2012.16.2003

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Virtual push-forwards

Cristina Manolache

Geometry & Topology 16 (2012) 2003–2036

DOI: 10.2140/gt.2012.16.2003

Abstract

Let $p : F \to G$ be a morphism of DM stacks of positive virtual relative dimension $k$ and let $γ \in A^{k} (F)$ . We give sufficient conditions for $p_{*} (γ \cdot {[F]}^{virt})$ 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

Volume 16, issue 4 (2012)