The arc space of horospherical varieties and motivic integration
Abstract
For arbitrary connected reductive group G we consider the motivic integral over the arc space of an arbitrary Q-Gorenstein horospherical G-variety associated with a colored fan and prove a formula for the stringy E-function of a horospherical variety X which generalizes the one for toric varieties. We remark that in contrast to toric varieties the stringy E-function of a Gorenstein horospherical variety X may be not a polynomial if some cones in the fan of X have nonempty sets of colors. Using the stringy E-function, we can formulate and prove a new smoothness criterion for locally factorial horospherical varieties. We expect that this smoothness criterion holds for arbitrary spherical varieties.
Keywords
Cite
@article{arxiv.1203.0671,
title = {The arc space of horospherical varieties and motivic integration},
author = {Victor Batyrev and Anne Moreau},
journal= {arXiv preprint arXiv:1203.0671},
year = {2012}
}
Comments
27 pages, the proofs of Proposition 2.4 and Theorem 3.1 have been substantially modified, a general argument was added in the proof of Lemma 5.4., to appear in Compositio Math