Mathematical Research Letters

Volume 18 (2011)

Number 4

Derived Resolution Property for Stacks, Euler Classes and Applications

Pages: 677 – 690



Yi Hu (Department of Mathematics, University of Arizona, USA)

Jun Li (Department of Mathematics, Stanford University, USA)


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 $\Pf$. 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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