Virtual push-forwards

Abstract

Let $p:F\to G$ be a morphism of stacks of positive \emph{virtual} relative dimension $k$ and let $\gamma \in H^k(F)$. We give sufficient conditions for $p_{\ast }\gamma \cdot [F{]}^{virt}$ to be a multiple of $[G{]}^{virt}$. We apply this result to 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.

References in corpus (2)

• The moduli space of stable quotients
• Moduli spaces of stable quotients and wall-crossing phenomena

Cited by in corpus (13)

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• Tautological stable pair invariants of Calabi-Yau 4-folds
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• Relative quasimaps and mirror formulae
• The local-orbifold correspondence for simple normal crossings pairs
• Tangent curves to degenerating hypersurfaces
• A new method toward the Landau-Ginzburg/Calabi-Yau correspondence via quasi-maps
• Quasimaps to moduli spaces of sheaves
• Stable maps and stable quotients
• Convergence of the mirror to a rational elliptic surface
• A remark on virtual pushforward properties in Gromov-Witten theory
• The log-open correspondence for two-component Looijenga pairs