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arXiv · 1301.3222

Divisors class groups of singular surfaces

Robin Hartshorne·Claudia Polini
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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 P^3. We apply these results to limit the possible curves that can be set-theoretic complete intersection in P^3 in characteristic zero.

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Robin Hartshorne, Claudia Polini. 2013-01-15. Divisors class groups of singular surfaces. https://arxiv.org/abs/1301.3222

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