Stable Ulrich bundles on cubic fourfolds

In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, dep...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Hoang Le Truong, Yen, Hoang Ngoc
Format: Article
Language:English
Subjects:
Mathematical analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, depending roughly on \(r\) parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new \(19\)-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold \(X\), there exist arithmetically Cohen-Macaulay smooth surface \(Y \subset X\) which are not an intersection \(X \cap T\) for a codimension two subvariety \(T \subset \Bbb P^5\).
ISSN:2331-8422