Geodesic
Toric hyperkähler varieties
Documenta mathematica, Tome 7 (2002), pp. 495-534.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Extending work of Bielawski-Dancer citeBD and Konno citeKo, we develop a theory of toric hyperkähler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkähler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov citeKP, are extended to the hyperkähler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima citeNa. 
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     author = {Hausel, Tam\'as and Sturmfels, Bernd},
     title = {Toric hyperk\"ahler varieties},
     journal = {Documenta mathematica},
     pages = {495--534},
     publisher = {mathdoc},
     volume = {7},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a4/}
}
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Hausel, Tamás; Sturmfels, Bernd. Toric hyperkähler varieties. Documenta mathematica, Tome 7 (2002), pp. 495-534. http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a4/