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

   

 

Tangent algebras


Authors: Aron Simis, Bernd Ulrich and Wolmer V. Vasconcelos
Journal: Trans. Amer. Math. Soc. 364 (2012), 571-594
MSC (2010): Primary 13A30, 13N05; Secondary 13B22, 14F10
Published electronically: September 14, 2011
MathSciNet review: 2846344
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Abstract: One studies the Zariski tangent cone $ T_X\stackrel{\pi}{\longrightarrow} X$ to an affine variety $ X$ and the closure $ \overline{T}_X$ of $ \pi^{-1}(\textrm{Reg}(X))$ in $ T_X$. One focuses on the comparison between $ T_X$ and $ \overline{T}_X$, giving sufficient conditions on $ X$ in order that $ T_X=\overline{T}_X$. One considers, in particular, the question of when this equality takes place in the presence of the reducedness of the Zariski tangent cone. Another problem considered here is to understand the impact of the Cohen-Macaulayness or normality of $ \overline{T}_X$ on the local structure of $ X$.


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Additional Information

Aron Simis
Affiliation: Departamento de Matemática, Universidade Federal de Pernambuco, 50740-540 Recife, PE, Brazil
Email: aron@dmat.ufpe.br

Bernd Ulrich
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email: ulrich@math.purdue.edu

Wolmer V. Vasconcelos
Affiliation: Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
Email: vasconce@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05161-5
Received by editor(s): November 25, 2007
Received by editor(s) in revised form: June 18, 2009
Published electronically: September 14, 2011
Additional Notes: The first author was partially supported by CNPq, Brazil
The second author was partially supported by the NSF, USA
The third author was partially supported by the NSF, USA
Article copyright: © Copyright 2011 American Mathematical Society