Toric Varieties of Schr\"oder Type

JiSun Huh ; Seonjeong Park

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 1, Tome 317 (2022), pp. 179-197.

Résumé

A dissection of a polygon is obtained by drawing diagonals such that no two diagonals intersect in their interiors. In this paper, we define a toric variety of Schröder type as a smooth toric variety associated with a polygon dissection. Toric varieties of Schröder type are Fano generalized Bott manifolds, and they are isomorphic if and only if the associated Schröder trees are the same as unordered rooted trees. We describe the cohomology ring of a toric variety of Schröder type using the associated Schröder tree and discuss the cohomological rigidity problem.

Détail

Keywords: toric variety, polygon dissection, Schröder tree, generalized Bott manifold.

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