The intrinsic normal cone

  title={The intrinsic normal cone
  author={Kai Behrend and Barbara Fantechi},
  journal={Inventiones mathematicae},
Abstract.Let $X$ be an algebraic stack in the sense of Deligne-Mumford. We construct a purely $0$-dimensional algebraic stack over $X$ (in the sense of Artin), the intrinsic normal cone ${\frak C}_X$. The notion of (perfect) obstruction theory for $X$ is introduced, and it is shown how to construct, given a perfect obstruction theory for $X$, a pure-dimensional virtual fundamental class in the Chow group of $X$. We then prove some properties of such classes, both in the absolute and in… Expand
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