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- Title
STABLE ULRICH BUNDLES.
- Authors
CASANELLAS, MARTA; HARTSHORNE, ROBIN; GEISS, FLORIAN; SCHREYER, FRANK-OLAF
- Abstract
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 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). We are also able to prove the existence of stable Ulrich bundles of any rank on nonsingular cubic threefolds in ℙ4, and we show that the restriction map from bundles on the threefold to bundles on the surface is generically étale and dominant.
- Subjects
EXISTENCE theorems; VECTOR bundles; ALGEBRAIC varieties; CUBIC surfaces; PROOF theory; MODULI theory; MATHEMATICAL analysis
- Publication
International Journal of Mathematics, 2012, Vol 23, Issue 8, p1250083-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X12500838