The arc space of horospherical varieties and motivic integration

Details The arc space of horospherical varieties and motivic integration The arc space of horospherical varieties and motivic integration

2012-03-03

arxiv.org/abs/1203.0671v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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.

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