Varieties with vanishing holomorphic Euler characteristic

A vanishing theorem for Fano varieties in positive characteristic

for i < d, where WΩdX is the sheaf of De Rham-Witt (DRW) differential forms of degree d constructed by Bloch and Illusie. This is because H(WOX)⊗K is the part of crystalline cohomology with Frobenius slopes in the interval [0, 1[, while Hi(W,WΩdX) is the part with slope d ([9] cor. II.3.5). The author gave an erroneous proof of this corollary (in fact, an integral version) in an earlier preprin...

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...

Exponentiation and Euler Characteristic

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...

Euler characteristic Galerkin scheme with recovery

— This paper describes a gênerai formulation of the Euler Characteristic Galerkin (ECG) scheme for scalar conservation laws, based on the theory of the Riemann-Stieltjes intégral. The ECG scheme is proved to be equivalent to the projection of Brenier' s transportcollapse operator. For the purpose of getting higher order accuracy, we explore two recovery procedures, namely continuous linear reco...