Zeta functions and 'Kontsevich invariants' on singular varieties
| dc.creator | Veys, Willem | |
| dc.date | 2000-03-03 | |
| dc.date | 2000-04-11 | |
| dc.date.accessioned | 2026-07-07T04:34:11Z | |
| dc.date.available | 2026-07-07T04:34:11Z | |
| dc.description | Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain 'motivic integral', living in a completion of the Grothendieck ring of algebraic varieties. He used this invariant to show that birational Calabi-Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the motivic (Igusa) zeta function, associated to a regular function on X, which specializes to both the classical p-adic Igusa zeta function and the topological zeta function, and also to Kontsevich's invariant. This paper treats a generalization to singular varieties. Batyrev already considered such a 'Kontsevich invariant' for log terminal varieties (on the level of Hodge polynomials instead of in the Grothendieck ring), and previously we introduced a motivic zeta function on normal surface germs. Here on any Q-Gorenstein variety X we associate a motivic zeta function and a 'Kontsevich invariant' to effective Q-Cartier divisors on X whose support contains the singular locus of X. | |
| dc.description | AMS-TeX (using PicTeX), 27 pages; some minor improvements | |
| dc.identifier | https://arxiv.org/abs/math/0003025 | |
| dc.identifier | http://arxiv.org/abs/math/0003025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58808 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14B05, 14E15, 32S50, 32S45 | |
| dc.title | Zeta functions and 'Kontsevich invariants' on singular varieties | |
| dc.type | text |