Stable Ulrich bundles

الأصل · EN

The existence of stable ACM vector bundles of high rank on algebraic varieties is a challenging problem. In this paper, we study stable Ulrich bundles (that is, stable ACM bundles whose corresponding module has the maximum number of generators) on nonsingular cubic surfaces X ⊂ P³. We give necessary and sufficient conditions on the first Chern class D for the existence of stable Ulrich bundles on X of rank r and c₁=D. When such bundles exist, we prove that that the corresponding moduli space of stable bundles is smooth and irreducible of dimension D²-2r²+1 and consists entirely of stable Ulrich bundles (see Theorem 1.1). As a consequence, we are also able to prove the existence of stable Ulrich bundles of any rank on nonsingular cubic threefolds in P⁴.