Ulrich partitions for two-step flag varieties

Coskun, Izzet; Jaskowiak, Luke

doi:10.2140/involve.2017.10.531

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Ulrich partitions for two-step flag varieties

Izzet Coskun and Luke Jaskowiak

Vol. 10 (2017), No. 3, 531–539

DOI: 10.2140/involve.2017.10.531

Abstract

Ulrich bundles play a central role in singularity theory, liaison theory and Boij–Söderberg theory. It was proved by the first author together with Costa, Huizenga, Miró-Roig and Woolf that Schur bundles on flag varieties of three or more steps are not Ulrich and conjectured a classification of Ulrich Schur bundles on two-step flag varieties. By the Borel–Weil–Bott theorem, the conjecture reduces to classifying integer sequences satisfying certain combinatorial properties. In this paper, we resolve the first instance of this conjecture and show that Schur bundles on $F (k, k + 3; n)$ are not Ulrich if $n > 6$ or $k > 2$ .

Keywords

flag varieties, Ulrich bundles, Schur bundles

Mathematical Subject Classification 2010

Primary: 14M15

Secondary: 14J60, 13C14, 13D02, 14F05

Milestones

Received: 12 May 2016

Accepted: 15 June 2016

Published: 14 December 2016

Communicated by Ravi Vakil

Authors

Izzet Coskun
Department of Mathematics, Statistics and CS University of Illinois at Chicago Chicago, IL 60607 United States

Luke Jaskowiak
Department of Mathematics, Statistics and CS University of Illinois at Chicago Chicago, IL 60607 United States

Vol. 10, No. 3, 2017