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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Tangent algebras
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by Aron Simis, Bernd Ulrich and Wolmer V. Vasconcelos PDF
Trans. Amer. Math. Soc. 364 (2012), 571-594 Request permission

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
  • MR Author ID: 162400
  • Email: aron@dmat.ufpe.br
  • Bernd Ulrich
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
  • MR Author ID: 175910
  • 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
  • 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
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 571-594
  • MSC (2010): Primary 13A30, 13N05; Secondary 13B22, 14F10
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05161-5
  • MathSciNet review: 2846344