Virtual fundamental classes, global normal cones and Fulton's canonical classes
Algebraic Geometry
2007-05-23 v1
Abstract
This paper, first written in 1997, aims at a simplified and more elementary construction of algebraic-geometric virtual fundamental classes as defined by Li/Tian and Behrend/Fantechi. We replace the use of Artin stacks in the latter approach by a yoga of cone bundles of possible independent interest. We also observe a formula for virtual fundamental classes involving only the total Chern class of the index bundle and Fulton's canonical class of the moduli space.
Cite
@article{arxiv.math/0509076,
title = {Virtual fundamental classes, global normal cones and Fulton's canonical classes},
author = {Bernd Siebert},
journal= {arXiv preprint arXiv:math/0509076},
year = {2007}
}
Comments
This version differs from the published text in correcting statements on mere dependence of cohomology rather than homotopy. These were based on a flawed splitting statement, as pointed out by Charles Cadman. Moreover, the proof of Proposition 2.11 required more attention. 16 pages