Type-A toric varieties may be obtained as GIT quotients with respect to a torus action with weights corresponding to roots of the group $ SL(k) $ for some $ k>1 $. These varieties appear in various important applications, in particular, as normal cones to strata in moduli spaces of vector bundles. In this paper, we describe the intersection Betti numbers of these varieties, and those of some associated projective varieties. We present an elegant combinatorial model for these numbers, and, using the work of Hausel and Sturmfels, we show that the relevant intersection cohomology groups are endowed with a canonical product structure.
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Keywords: toric varieties, intersection cohomology, acyclic graphs
Szenes, Andras 1; Trapeznikova, Olga 1
CC-BY 4.0
@article{ALCO_2025__8_2_575_0,
author = {Szenes, Andras and Trapeznikova, Olga},
title = {Intersection cohomology of {type-A} toric varieties},
journal = {Algebraic Combinatorics},
pages = {575--596},
publisher = {The Combinatorics Consortium},
volume = {8},
number = {2},
year = {2025},
doi = {10.5802/alco.417},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.417/}
}
TY - JOUR AU - Szenes, Andras AU - Trapeznikova, Olga TI - Intersection cohomology of type-A toric varieties JO - Algebraic Combinatorics PY - 2025 SP - 575 EP - 596 VL - 8 IS - 2 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.417/ DO - 10.5802/alco.417 LA - en ID - ALCO_2025__8_2_575_0 ER -
%0 Journal Article %A Szenes, Andras %A Trapeznikova, Olga %T Intersection cohomology of type-A toric varieties %J Algebraic Combinatorics %D 2025 %P 575-596 %V 8 %N 2 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.417/ %R 10.5802/alco.417 %G en %F ALCO_2025__8_2_575_0
Szenes, Andras; Trapeznikova, Olga. Intersection cohomology of type-A toric varieties. Algebraic Combinatorics, Volume 8 (2025) no. 2, pp. 575-596. doi : 10.5802/alco.417. https://alco.centre-mersenne.org/articles/10.5802/alco.417/
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