Motivic zeta functions for curve singularities

DOI10.1215/00277630-2009-007zbMath1252.14019arXiv0903.1238OpenAlexW2962938468MaRDI QIDQ3578027

Julio José Moyano-Fernández, Wilson A. Zuniga-Galindo

Publication date: 13 July 2010

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.1238

zbMATH Keywords

Poincaré serieszeta functionslocal ringmotivic zeta functionplane curve singularitiesalgebraic curves over positive characteristicsemigroup of curve singularities

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Singularities of curves, local rings (14H20) Zeta functions and (L)-functions (11S40) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40)

Related Items (7)

Generalized Poincaré series for plane curve singularities ⋮ Hilbert function, generalized Poincaré series and topology of plane valuations ⋮ On Weierstrass semigroups at one and two points and their corresponding Poincaré series ⋮ Generalised Poincaré series and embedded resolution of curves ⋮ Poincaré series for curve singularities and its behaviour under projections ⋮ Fractional ideals and integration with respect to the generalised Euler characteristic ⋮ On Poincaré series of singularities of algebraic curves over finite fields

Cites Work

• Gorenstein curves and symmetry of the semigroup of values
• Functional equations for zeta functions of non-Gorenstein orders in global fields
• Multi-index filtrations and generalized Poincaré series
• The semigroup of values of a curve singularity with several branches
• La fonction zeta d'une monodromie
• Local and global zeta-functions of singular algebraic curves
• Germs of arcs on singular algebraic varieties and motivic integration
• Gorenstein property and symmetry for one-dimensional local Cohen-Macaulay rings
• Zeta functions and Cartier divisors on singular curves over finite fields
• The Alexander polynomial of a plane curve singularity via the ring of functions on it
• On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions
• Equivalence relations on algebraic curves
• Generalized jacobian varieties
• An introduction to motivic zeta functions of motives
• On the relation between the generalized Poincaré series and the Stöhr zeta function
• Caracteristiques D'Euler-Poincare, Fonctions Zeta Locales et Modifications Analytiques
• On the poles of regular differentials of singular curves
• Derived Varieties of Complexes and Kostant’s Theorem for $$\mathfrak{gl}(\mathrm{m}|\mathrm{n})$$
• THE ALEXANDER POLYNOMIAL OF A PLANE CURVE SINGULARITY AND INTEGRALS WITH RESPECT TO THE EULER CHARACTERISTIC
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