On the arithmetical rank of certain segre embeddings
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Abstract:
We study the number of (set-theoretically) defining equations of Segre products of projective spaces times certain projective hypersurfaces, extending results by Singh and Walther. Meanwhile, we prove some results about the cohomological dimension of certain schemes. In particular, we solve a conjecture of Lyubeznik about an inequality involving the cohomological dimension and the étale cohomological dimension of a scheme, in the characteristic-zero-case and under a smoothness assumption. Furthermore, we show that a relationship between depth and cohomological dimension discovered by Peskine and Szpiro in positive characteristic also holds true in characteristic-zero up to dimension three.References
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Additional Information
- Matteo Varbaro
- Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Balbi, 5, 16216 Genova, Italy
- MR Author ID: 873871
- Email: varbaro@dima.unige.it
- Received by editor(s): April 14, 2010
- Received by editor(s) in revised form: July 26, 2010, and July 30, 2010
- Published electronically: April 30, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 5091-5109
- MSC (2010): Primary 14F17, 13D05, 13D45, 14A25
- DOI: https://doi.org/10.1090/S0002-9947-2012-05435-3
- MathSciNet review: 2931323