Mathematics – Symplectic Geometry
Scientific paper
2001-06-27
Osaka J. Math. 40 (2003), 1-68
Mathematics
Symplectic Geometry
Scientific paper
We introduce the notion of a multi-fan. It is a generalization of that of a fan in the theory of toric variety in algebraic geometry. Roughly speaking a toric variety is an algebraic variety with an action of algebraic torus of the same dimension as that of the variety, and a fan is a combinatorial object associated with the toric variety. Algebro-geometric properties of the toric variety can be described in terms of the associated fan. We develop a combinatorial theory of multi-fans and define ``topological invariants'' of a multi-fan. A smooth manifold with an action of a compact torus of half the dimension of the manifold and with some orientation data is called a torus manifold. We associate a multi-fan with a torus manifold, and apply the combinatorial theory to describe topological invariants of the torus manifold. A similar theory is also given for torus orbifolds. As a related subject a generalization of the Ehrhart polynomial concerning the number of lattice points in a convex polytope is discussed.
hattori Akio
Masuda Mikiya
No associations
LandOfFree
Theory of multi-fans does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Theory of multi-fans, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Theory of multi-fans will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-406623