Mathematical Research Letters
Volume 18 (2011)
Derived Resolution Property for Stacks, Euler Classes and Applications
Pages: 677 – 690
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.