Konferenz: Swiss-Russian Seminar on Moduli Spaces and Physics


Motivic integration

{{_Ltalk:R}} E. Gorsky
Datum: 06.12.07   Zeit: 15.10 - 16.10   Raum: Y27H36

Abstract: Motivic integration is the integration over the space of formal germs of parametrized curves on a given variety. On the plane, germs of (reducible) curves are in one-to-one correspondence with germs of functions as its zero level sets. Motivic measure on the space of functions was introduced by Campillo, Delgado and Gusein-Zade as an analog of the motivic measure on the space of arcs. It turns out that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integrals over the space of functions as integrals over the union of all symmetric powers of the space of arcs. For example, this method gives a formula for a "motivic analogue" of the Alexander polynomial of an algebraic link. In some sence, this correspondence may be considered as an infinitesimal algebraic version of the target space -- worldsheet correspondence in string theory.