2022/06/10 by Hoang Le Truong, Truong, Hoang Le, Hoang Ngoc Yen +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2206.05285
openalex publication_date 2022/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≥ 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 ⊂ X which are not an intersection X ∩ T for a codimension two subvariety T ⊂ \Bbb P5.