Divisors class groups of singular surfaces
Commutative Algebra
2013-01-16 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1301.3222,
title = {Divisors class groups of singular surfaces},
author = {Robin Hartshorne and Claudia Polini},
journal= {arXiv preprint arXiv:1301.3222},
year = {2013}
}