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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the arithmetical rank of certain segre embeddings


Author: Matteo Varbaro
Journal: Trans. Amer. Math. Soc. 364 (2012), 5091-5109
MSC (2010): Primary 14F17, 13D05, 13D45, 14A25
Published electronically: April 30, 2012
MathSciNet review: 2931323
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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.


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Additional Information

Matteo Varbaro
Affiliation: Dipartimento di Matematica, Università degli Studi di Genova, Via Balbi, 5, 16216 Genova, Italy
Email: varbaro@dima.unige.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05435-3
PII: S 0002-9947(2012)05435-3
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.