EULER CHARACTERISTIC OF SPRINGER FIBERS

Smooth Components of Springer Fibers

This article studies components of Springer fibers for gl(n) that are associated to closed orbits of GL(p) × GL(q) on the flag variety of GL(n), n = p+ q. These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the ...

Purity of Equivalued Affine Springer Fibers

The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its homology is “pure”.

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...

The Euler Characteristic of an Enriched Category

We develop the homotopy theory of Euler characteristic (magnitude) of a category enriched in a monoidal model category. If a monoidal model category V is equipped with an Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler characteristic of V-enriched categories is also compatible with weak equivalences and fibrations in the canonical model structu...