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 the relative context. Via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory, and sometimes a perfect one.
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Oblatum 26-II-1996 & 27-VI-1996
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Behrend, K., Fantechi, B. The intrinsic normal cone . Invent math 128, 45–88 (1997). https://doi.org/10.1007/s002220050136
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DOI: https://doi.org/10.1007/s002220050136