Toric hyperkähler varieties.
Hausel, Tamás, Sturmfels, Bernd (2002)
Documenta Mathematica
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Hausel, Tamás, Sturmfels, Bernd (2002)
Documenta Mathematica
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Tamás Hausel (2005)
Open Mathematics
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Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely...
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).
Sato, Hiroshi (2003)
International Journal of Mathematics and Mathematical Sciences
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Emili Bifet (1992)
Publicacions Matemàtiques
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We explain the philosophy behind the computations in [BDP] and place them in a wider conceptual setting. We also outline, for toric varieties, the resulting equivalent approach to some key results in that theory.
Markus P. Brodmann (1987)
Časopis pro pěstování matematiky
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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...
Kędzierski, Oskar (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30. In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to...
Walter Lawrence Griffith, Jr. (1982)
Colloquium Mathematicae
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Matthias Franz, Andrzej Weber (2005)
Annales de l’institut Fourier
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We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic -variety ( being a connected algebraic group) in terms of its equivariant cohomology provided that is pure. This is the case, for example, if is smooth and has only finitely many orbits. We work...