Stable Ulrich bundles on cubic fourfolds

In this paper, we examine the presence of Ulrich bundles on cubic fourfolds. We establish necessary and sufficient conditions for the existence of Ulrich bundles of a specific rank r . As a consequence, we show the existence of a family of non-decomposable Ulrich bundles of rank r on certain cubic f...

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Bibliographic Details
Published in:	Manuscripta mathematica Vol. 174; no. 1-2; pp. 243 - 267
Main Authors:	Hoang, Truong Le, Hoang, Yen Ngoc
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-05-2024 Springer Nature B.V
Subjects:	Algebraic Geometry Calculus of Variations and Optimal Control; Optimization Geometry Lie Groups Mathematics Mathematics and Statistics Number Theory Topological Groups 14M05 13C40 Secondary 14J25 14J60 14M06 Primary 13C14 13D02
Online Access:	Get full text
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Summary:	In this paper, we examine the presence of Ulrich bundles on cubic fourfolds. We establish necessary and sufficient conditions for the existence of Ulrich bundles of a specific rank r . As a consequence, we show the existence of a family of non-decomposable Ulrich bundles of rank r on certain cubic fourfolds, which are dependent on approximately r parameters and have wild representation type. Our study also encompasses examples of arithmetically Cohen–Macaulay smooth surfaces that are not intersections of cubic fourfolds and codimension two subvarieties.
ISSN:	0025-2611 1432-1785
DOI:	10.1007/s00229-023-01499-y