Rational smoothness, cellular decompositions and GKM theory

Gonzales, Richard¹

¹ Faculty of Engineering and Natural Sciences, Sabancı Üniversitesi, Orhanli, Tuzla, 34956 Istanbul, Turkey

Geometry & topology, Tome 18 (2014) no. 1, pp. 291-326.

Résumé

We introduce the notion of $\mathbb{Q}$–filtrable varieties: projective varieties with a torus action and a finite number of fixed points, such that the cells of the associated Bialynicki-Birula decomposition are all rationally smooth. Our main results develop GKM theory in this setting. We also supply a method for building nice combinatorial bases on the equivariant cohomology of any $\mathbb{Q}$–filtrable GKM variety. Applications to the theory of group embeddings are provided.

Détail

DOI : 10.2140/gt.2014.18.291

Classification : 14F43, 14L30, 55N91, 14M15
Keywords: rational smoothness, algebraic torus actions, GKM theory, equivariant cohomology, algebraic monoids, group embeddings

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