Vol. 10, No. 3, 2017

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ISSN: 1944-4184 (e-only)
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Ulrich partitions for two-step flag varieties

Izzet Coskun and Luke Jaskowiak

Vol. 10 (2017), No. 3, 531–539
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