Derived resolution property for stacks, Euler classes and applications

Yi Hu; Jun Li

doi:10.4310/MRL.2011.v18.n4.a7

Derived resolution property for stacks, Euler classes and applications

Yi Hu
, Jun Li

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in ℙ⁴. These numbers are conjectured to be the reduced Gromov-Witten invariants and to determine the usual Gromov-Witten numbers of the smooth quintic as speculated by J. Li and A. Zinger.

Original language	English (US)
Pages (from-to)	677-690
Number of pages	14
Journal	Mathematical Research Letters
Volume	18
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2011.v18.n4.a7
State	Published - Jul 2011

ASJC Scopus subject areas

General Mathematics

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10.4310/MRL.2011.v18.n4.a7

Cite this

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abstract = "By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in ℙ4. These numbers are conjectured to be the reduced Gromov-Witten invariants and to determine the usual Gromov-Witten numbers of the smooth quintic as speculated by J. Li and A. Zinger.",

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AB - By resolving any perfect derived object over a Deligne-Mumford stack, we define its Euler class. We then apply it to define the Euler numbers for a smooth Calabi-Yau threefold in ℙ4. These numbers are conjectured to be the reduced Gromov-Witten invariants and to determine the usual Gromov-Witten numbers of the smooth quintic as speculated by J. Li and A. Zinger.

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Derived resolution property for stacks, Euler classes and applications

Abstract

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