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arXiv · 2409.01379

Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch

Aiden Suter·Ben Webster
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Abstract

Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities. In this paper, we give a concrete construction of this tilting generator on the cotangent bundle of $Gr(2,4)$, the Grassmannian of 2-planes in $\mathbb{C}^4$. This construction builds on work of the second author describing these tilting bundles in terms of KLRW algebras, but in this low-dimensional case, we are able to describe our tilting generator as a sum of geometrically natural bundles on $T^*Gr(2,4)$: line bundles and their extensions, as well as the tautological bundle and its perpendicular.

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Aiden Suter, Ben Webster. 2024-09-02. Tilting Generator for the $T^*Gr(2,4)$ Coulomb Branch. https://arxiv.org/abs/2409.01379

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