[Base d'Hilbert du semigroupe de Lipman]
Dans ce travail, nous donnons une nouvelle méthode pour calculer les générateurs du semigroupe de certains diviseurs positifs a support sur le diviseur exceptionnel d'une singularité de surface normale. Notre approche est purement combinatoire et permet d'éviter le calcul difficile des invariants de l'anneau tel qu'il est présenté dans le travail de Altınok et Tosun.
In this Note, we give a new method to compute the Hilbert basis of the semigroup of certain positive divisors supported on the exceptional divisor of a normal surface singularity. Our approach is purely combinatorial and enables us to avoid the long calculation of the invariants of the ring as it is presented in the work of Altınok and Tosun.
Accepté le :
Publié le :
@article{CRMATH_2010__348_23-24_1311_0,
author = {\c{S}ahin, Mesut},
title = {Hilbert basis of the {Lipman} semigroup},
journal = {Comptes Rendus. Math\'ematique},
pages = {1311--1314},
publisher = {Elsevier},
volume = {348},
number = {23-24},
year = {2010},
doi = {10.1016/j.crma.2010.11.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.11.005/}
}
TY - JOUR AU - Şahin, Mesut TI - Hilbert basis of the Lipman semigroup JO - Comptes Rendus. Mathématique PY - 2010 SP - 1311 EP - 1314 VL - 348 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.11.005/ DO - 10.1016/j.crma.2010.11.005 LA - en ID - CRMATH_2010__348_23-24_1311_0 ER -
Şahin, Mesut. Hilbert basis of the Lipman semigroup. Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1311-1314. doi : 10.1016/j.crma.2010.11.005. http://www.numdam.org/articles/10.1016/j.crma.2010.11.005/
[1] Generators for semigroup of Lipman, Bull. Braz. Math. Soc., Volume 39 (2008) no. 1, pp. 123-135
[2] On isolated rational singularities of surfaces, Amer. J. Math., Volume 88 (1966), pp. 129-136
[3] On simplicial toric varieties which are set-theoretic complete intersections, J. Algebra, Volume 226 (2000) no. 2, pp. 880-892
[4] CoCoA: a system for doing computations in commutative algebra http://cocoa.dima.unige.it (available at)
[5] Explicit horizontal open books on some plumbings, Internat. J. Math., Volume 17 (2006) no. 9, pp. 1013-1031
[6] 4ti2 team, 4ti2: A software package for algebraic, geometric and combinatorial problems on linear spaces, available at www.4ti2.de.
[7] Introduction to toric varieties, The William H. Roever Lectures in Geometry, Annals of Mathematics Studies, vol. 131, Princeton University Press, Princeton, NJ, 1993
[8] Gröbner bases of simplicial toric ideals, Nagoya Math. J., Volume 196 (2009), pp. 67-85
[9] On the computation of Hilbert bases of cones, Mathematical Software, Beijing, 2002, World Sci. Publ., River Edge, NJ, 2002, pp. 307-317
[10] Toric sets and orbits on toric varieties, J. Pure Appl. Algebra, Volume 181 (2003) no. 1, pp. 75-83
[11] Computational Commutative Algebra 2, Springer-Verlag, Berlin, 2005
[12] On rational singularities, Amer. J. Math., Volume 94 (1972), pp. 597-608
[13] Rational singularities, with applications to algebraic surfaces and unique factorization, Publ. Math. IHES, Volume 36 (1969), pp. 195-279
[14] Poincaré series associated with surface singularities, Singularities I, Contemp. Math., vol. 474, Amer. Math. Soc., Providence, RI, 2008, pp. 271-297
[15] Lattice cohomology of normal surface singularities, Publ. Res. Inst. Math. Sci., Volume 44 (2008) no. 2, pp. 507-543
[16] H. Pinkham, Singularités rationnelles de surfaces, in: Séminaire sur les singularités des surfaces, vol. 777, Springer-Verlag, 1980, pp. 147–178.
[17] Gröbner Bases and Convex Polytopes, Univ. Lecture Ser., vol. 8, Amer. Math. Soc., Providence, RI, 1996
[18] Tyurina components and rational cycles for rational singularities, Turkish J. Math., Volume 23 (1999) no. 3, pp. 361-374
Cité par Sources :
