The intrinsic normal cone

@article{Behrend1997TheIN,
  title={The intrinsic normal cone
},
  author={K. Behrend and B. Fantechi},
  journal={Inventiones mathematicae},
  year={1997},
  volume={128},
  pages={45-88}
}
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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References

SHOWING 1-10 OF 33 REFERENCES
Functors of Artin rings
Versal deformations and algebraic stacks
Algebraic Geometry: A First Course
Enumeration of Rational Curves Via Torus Actions
Techniques de construction et th'eor'emes d''existence en g'eom'etrie alg'ebrique
Unobstructed deformations
  • II. J. Algebraic Geometry, 4:277{279
  • 1995
...
1
2
3
4
...