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Divisor class groups of singular surfaces


Authors: Robin Hartshorne and Claudia Polini
Journal: Trans. Amer. Math. Soc. 367 (2015), 6357-6385
MSC (2010): Primary 14C20, 13A30; Secondary 14M10, 14J17
DOI: https://doi.org/10.1090/S0002-9947-2015-06228-X
Published electronically: January 15, 2015
MathSciNet review: 3356940
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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 $ \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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Additional Information

Robin Hartshorne
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: robin@math.berkeley.edu

Claudia Polini
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: cpolini@nd.edu

DOI: https://doi.org/10.1090/S0002-9947-2015-06228-X
Received by editor(s): March 19, 2013
Received by editor(s) in revised form: June 26, 2013
Published electronically: January 15, 2015
Additional Notes: The second author was partially supported by the NSA and the NSF
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.