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.

Published 19 August 2011