Constraints for the normality of monomial subrings and birationality
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- by Aron Simis and Rafael H. Villarreal PDF
- Proc. Amer. Math. Soc. 131 (2003), 2043-2048 Request permission
Abstract:
Let $k$ be a field and let ${\mathbf F}\subset k[x_1,\ldots ,x_{n}]$ be a finite set of monomials whose exponents lie on a positive hyperplane. We give necessary conditions for the normality of both the Rees algebra $R[\mathbf {F}t]$ and the subring $k[\mathbf {F}]$. If the monomials in $\mathbb {F}$ have the same degree, one of the consequences is a criterion for the $k$-rational map $F\colon {\mathbb P}^{n-1}_k \rightdasharrow {\mathbb P}^{m-1}_k$ defined by $\mathbf {F}$ to be birational onto its image.References
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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
- Rafael H. Villarreal
- Affiliation: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 México City, D.F., Mexico
- Email: vila@esfm.ipn.mx
- Received by editor(s): September 10, 2001
- Received by editor(s) in revised form: March 7, 2002
- Published electronically: November 13, 2002
- Additional Notes: The first author was partially supported by a CNPq grant and PRONEX-ALGA (Brazilian Group in Commutative Algebra and Algebraic Geometry)
The second author was supported in part by CONACyT grant 27931E. This author thanks PRONEX-ALGA for their hospitality - Communicated by: Wolmer V. Vasconcelos
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2043-2048
- MSC (2000): Primary 13H10; Secondary 14E05, 14E07, 13B22
- DOI: https://doi.org/10.1090/S0002-9939-02-06790-4
- MathSciNet review: 1963748