Characteristic classes for Schubert varieties and torus action
speaker: Andrzej Weber (University of Warsaw)abstract: The Hirzebruch class of a complex manifold is characteristic class whose integral is equal to the $\chiy$-genus. The construction admits a generalization for singular varieties. The equivariant version of the Hirzebruch class can be developed as well. The general theory applied in the situation when a torus acts on a singular variety allows to apply tools as Localization Theorem of Atiyah-Bott and Berline-Vergne. We obtain a meaningful invariant of a germ of singularity. When it is made explicit it turns out that the result is just a polynomial in characters of the torus. In particular, the Hirzebruch class can be computed for combinatorially defined objects. Among others the toric varieties or Schuber cells are of special interest. The issue of positivity of coefficients in a certain expansion remains mysterious.
timetable:
Fri 20 Feb, 11:30 - 12:10, Aula Dini
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