SL2 actions and cohomology of Schubert varieties
E. Akyildiz (1990)
Banach Center Publications
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E. Akyildiz (1990)
Banach Center Publications
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Roy Joshua, Michel Brion (2004)
Journal of the European Mathematical Society
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We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.
Peter Schneider (1992)
Mathematische Annalen
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Matthias Franz (2010)
Colloquium Mathematicae
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Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated...
Kahn, Bruno (1996)
Documenta Mathematica
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A. Silverberg, Yu. G. Zarhin (2001)
Bulletin de la Société Mathématique de France
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In this paper we study the étale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable over a quadratic extension) in terms of the action of the absolute inertia group on the étale cohomology groups with finite coefficients.
Andrzej Weber (2004)
Open Mathematics
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We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain results concerning Koszul duality: nonequivariant intersection cohomology is equal to the cohomology of the Koszul complexIH T*(X)⊗H*(T). We also describe the weight filtration inIH *(X).
F. Kirwan (1987)
Inventiones mathematicae
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Walter Lawrence Griffith, Jr. (1982)
Colloquium Mathematicae
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M. Brodmann (1991)
Mathematische Zeitschrift
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F. Kirwan (1986)
Inventiones mathematicae
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Michael Harris, Steven Zucker (1994)
Inventiones mathematicae
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Karl-Heinz Fieseler (1991)
Journal für die reine und angewandte Mathematik
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H.H. Andersen (1985)
Inventiones mathematicae
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Mathias Peternell (1990)
Mathematische Annalen
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Lee, Min Ho (2008)
Beiträge zur Algebra und Geometrie
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