Unitary toric manifolds, multi-fans and equivariant index

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概要

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• We develop the theory of toric varieties from a topological point of view using equivariant cohomology. Indeed, we introduce a geometrical object called a unitary toric manifold and associate a combinatorial object called a multi-fan to it. This generalizes (in one direction) the well-known correspondence between a compact nonsingular toric variety and a (regular) fan. The multi-fan is a collection of cones is essentially the Todd genus of the unitary toric manifold. Since the Todd genus of a compact nonsingular toric variety is one, this explains why cones do not overlap in a usual fan. A moment map relates a unitary toric manifold equipped with an equivariant complex line bundle to a “twisted polytope”, and the equivariant Riemann-Roch index for the equivariant line bundle can be described in terms of the moment map. We apply this result to establish a generalizaation of Picks formula.

• 東北大学の論文

著者

• Masuda Mikiya

  Department Of Mathematics Osaka City University

関連論文

• An invariant of manifold pairs and its applications
• Unitary toric manifolds, multi-fans and equivariant index
• On the nonuniqueness of equivariant connected sums

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