Abstract
We study Cartier divisors on normal varieties with the action of a reductive groupG. We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local structure and the intersection theory of aG-variety. In particular, we prove an integral formula for the degree of an ample divisor on a variety of complexity 1, and apply this formula to computing the degree of a closed 3-dimensional orbit in any SL2-module.
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Timashev, D.A. Cartier divisors and geometry of normalG-varieties. Transformation Groups 5, 181–204 (2000). https://doi.org/10.1007/BF01236468
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DOI: https://doi.org/10.1007/BF01236468