The universal Euler characteristic for varieties of characteristic zero

The Equivariant Euler Characteristic of Real Coxeter Toric Varieties

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locus TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a gen...

The Euler Characteristic

I will describe a few basic properties of the Euler characteristic and then I use them to prove special case of a cute formula due to Bernstein-Khovanskii-Koushnirenko. 1. Basic properties of the Euler characteristic The Euler characteristic is a function χ which associates to each reasonable topological space X an integer χ(X). For us a reasonable space would be a space which admits a finite s...

Characteristic Varieties of Arrangements

The k Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, Vk(A), of the complex algebraic torus (C). In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of Vk(A). For any arrangement A, we show that the tangent cone at the identity of the...

A Formula for the Euler Characteristic Of

In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods , such as the enumeration of the graphs involved in a suitable stratification of M 2,n .

Exponentiation and Euler Characteristic