Divisor class groups of singular surfaces

Hartshorne, Robin; Polini, Claudia

doi:10.1090/S0002-9947-2015-06228-X

Divisor class groups of singular surfaces
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by Robin Hartshorne and Claudia Polini PDF

Trans. Amer. Math. Soc. 367 (2015), 6357-6385 Request permission

Abstract:

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne’s theorem for the cubic ruled surface in $\mathbb P^3$. We apply these results to limit the possible curves that can be set-theoretic complete intersections in $\mathbb P^3$ in characteristic zero.

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