Equivariant Hirzebruch class for singular varieties

Andrzej Weber ^[1]
1. [1] Warsaw University
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 3, 2016, págs. 1413-1454
Idioma: inglés
DOI: 10.1007/s00029-015-0214-x
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Resumen
- We develop an equivariant version of the Hirzebruch class for singular varieties. When the group acting is a torus we apply localization theorem of Atiyah–Bott and Berline–Vergne. The localized Hirzebruch class is an invariant of a singularity germ. The singularities of toric varieties and Schubert varieties are of special interest. We prove certain positivity results for simplicial toric varieties. The positivity for Schubert varieties is illustrated by many examples, but it remains mysterious.