Divisor class groups of singular surfaces
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- by Robin Hartshorne and Claudia Polini PDF
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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.References
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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
- MR Author ID: 340709
- Email: cpolini@nd.edu
- 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
- © Copyright 2015
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3356940