Stable Ulrich bundles on Fano threefolds with Picard number 2

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Genc O.

JOURNAL OF PURE AND APPLIED ALGEBRA, vol.222, no.1, pp.213-240, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 222 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1016/j.jpaa.2017.03.013
  • Journal Name: JOURNAL OF PURE AND APPLIED ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.213-240
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of P-3, Q (smooth quadric in P-4), V-3 (smooth cubic in P-4) or V-4 (complete intersection of two quadrics in P-5) along a smooth irreducible curve. We prove that the only class which admits Ulrich line bundles is the one obtained by blowing up a genus 3, degree 6 curve in P-3. Also, we prove that there exist stable rank two Ulrich bundles with c(1) = 3H on a generic member of this deformation class. (C) 2017 Elsevier B.V. All rights reserved.