A RATIO OF INTEGRATION BETWEEN QUOTIENTS IN GEOMETRIC INVARIANT THEORY

作者：Maddock Zachary^*

来源：Transformation Groups, 2014, 19(1): 131-158.

DOI：10.1007/s00031-014-9252-2

Let T be a maximal torus of a connected reductive group G that acts linearly on a projective variety X so that all semi-stable points are stable. This paper compares the integration on the geometric invariant theory quotient X//G of Chow classes sigma to the integration on the geometric invariant theory quotient X//T of certain lifts of sigma twisted by c (top)(g/t), the top Chern class of the T-equivariant vector bundle induced by the quotient of the adjoint representation on the Lie algebra of G by that of T. We provide a purely algebraic proof that the ratio between any two such integrals is an invariant of the group G and that it equals the order of the Weyl group whenever the root system of G decomposes into irreducible root systems of type A (n) , for various . As a corollary, we are able to remove this restriction on root systems by applying a related result of Martin from symplectic geometry.

• 出版日期2014-3