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arXiv · 1507.00102

Equivariant Ulrich bundles on flag varieties

Izzet Coskun·Jack Huizenga·Matthew Woolf
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Abstract

In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with respect to the minimal ample class. We classify Ulrich bundles of this form on two-step flag varieties F(2,n;n+1), F(2,n;n+2), F(k,k+1;n), and F(k,k+2;n). We give a conjectural description of the two-step flag varieties which admit such Ulrich bundles. Our results provide counterexamples to conjectures by Costa and Miro-Roig.

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Izzet Coskun, Jack Huizenga, Matthew Woolf. 2015-07-01. Equivariant Ulrich bundles on flag varieties. https://arxiv.org/abs/1507.00102

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