arXiv subjects
Publications and source records attributed to Xuanchun Lu.
We introduce virtual classes in the sense of Behrend-Fantechi, explaining how these directly generalize Fulton's localized top Chern class. We derive Siebert's formula for a virtual class on any Deligne-Mumford stack with a perfect obstruction theory having a global resolution.
For a DM-type morphism of algebraic stacks $f \colon X \to Y$ with a relative perfect obstruction theory $\mathbb{E} \to \mathbb{L}_{X/Y}$ having a global resolution, we give a formula for the induced virtual pullback in terms of $\mathbb{E}$ and $f$. We apply our formula to prove functoriality properties of the virtual fundamental class in Gromov-Witten theory.