Complutense University Library

On the Log-Canonical Threshold for Germs of Plane Curves

Artal Bartolo, Enrique and Cassou-Noguès, Pierrette and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2008) On the Log-Canonical Threshold for Germs of Plane Curves. In Singularities I: Algebraic and Analytic Aspects. American Mathematical Society , Cuernavaca, México, pp. 1-14. ISBN 978-0-8218-4458-8

[img] PDF
Restricted to Repository staff only until 31 December 2020.

255kB

Official URL: http://www.mat.ucm.es/~amelle/logcan-prep07-17.pdf

View download statistics for this eprint

==>>> Export to other formats

Abstract

In this article we show that for a given, reduced or non reduced, germ of a complex plane curve, there exists a local system of coordinates such that its log-canonical threshold at the singularity can be explicitly computed from the intersection of the boundary of its Newton polygon in such coordinates (degenerated or not) with the diagonal line.

Item Type:Book Section
Additional Information:Conference: International Conference on Geometry and Topology of Singularities Location: Cuernavaca, MEXICO Date: JAN 08-26, 2007-2008
Uncontrolled Keywords:Log-canonical threshold; Eisenbud-Neumman diagrams; topological zeta function
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16530
References:

M. Aprodu and D. Naie Log-canonical threshold for curves on a smooth surface, Preprint available at arXiv:math.AG/0707.0783.

E. Artal-Bartolo, Pi. Cassou-Noguès, I. Luengo and A. Melle-Hernández, Quasiordinary singularities and their zeta functions, Memoirs of the Amer. Math. Soc. 178 (2005),no. 841. Pi. Cassou-Noguès, Algebraic Curves, Book in preparation.

Pi. Cassou-Noguès, A. Libgober, Computations of polytopes of quasiadjunction, in preparation.

J. Denef and F. Loeser, Caractéristiques d’Euler-Poincaré, fonctions zeta locales et modifications analytiques, J. Amer. Math. Soc. 5 (1992), no.4, 705-720.

F. Ehlers and K. C. Luo, Minimal characteristic exponent of the Gauss-Manin connection of isolated singular point and Newton polyhedra, Math. Ann. 259 (1982), 431–441.

D. Eisenbud and W. Neumann, Three-Dimensional Link Theory and Invariants of Plane Curve Singularities, Ann. of Math. Studies 110, Princeton University Press, (1985).

J. Kollár, Singularities of pairs, Algebraic Geometry, Santa Cruz 1995, Proc. Sympos. Pure Math. 62 Amer. Math. Soc., Providence, RI, 1997.

B. Lichtin, Poles of |f(z,w)|2s and roots of the b-function, Ark. Mat. 27 (1989), no. 2, 283–304.

B. Malgrange, Polynôme de Bernstein-Sato et cohomologie évanescente, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque 101–102 (1983), 243–267.

C. Reydy, Étude d’invariants des germs de courbes planes à l’aide des diagrammes de Newton, Thèse de Doctorat, Bourdeaux, 2002.

M. Saito, Exponents and Newton polyhedra of isolated hypersurface singularities, Math. Ann. 281 (1988), 411–417.

M. Saito, On Microlocal b-function, Bull. Soc. math. France 122 (1994),163–184.

A.N. Varchenko, Asymptotic Hodge structure in the vanishing cohomology, Math. USSR Izvestija 18 (1982), 469–512.

W. Veys, Determination of the poles of the topological zeta function for curves, Manuscripta Math. 87 (1995), 435–448.

W. Veys, Zeta functions for curves and log-canonical models, Proc. London Math. Soc. 74 (1997), 360–378.

T. Yano, b-functions and exponents of hypersurface isolated singularities. Singularities, Part 2 (Arcata, Calif., 1981), 641–652, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.

Deposited On:26 Sep 2012 08:00
Last Modified:07 Feb 2014 09:31

Repository Staff Only: item control page