ACM bundles on cubic surfaces

By Marta Casanellas, Robin Hartshorne. 2008

98 citations recorded by the source corpus.

In this paper we prove that, for every r = 2, the moduli space MsX (r; c1,c2) of rank r stable vector bundles with Chern classes c1 = rH and c2 = 1/2 (3r2 - r) on a nonsingular cubic surface X ? P3 contains a nonempty smooth open subset formed by ACM bundles, i.e. vector bundles with no intermediate cohomology. The bundles we consider for this study are extremal for the number of generators of the corresponding module (these are known as Ulrich bundles), so we also prove the existence of indecomposable Ulrich bundles of arbitrarily high rank on X.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a870aac57f5806479b6655bfe6f6d4d956684c79

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In Algebra and Number Theory

1. Rosa M. Mir'o-Roig Joan Pons-Llopis
2. G. Casnati
3. R. Mir'o-Roig
4. J. Pons-Llopis
5. Emre Coskun
6. Rajesh S. Kulkarni
7. Yusuf Mustopa
8. L. Costa

In Computational Theory and Mathematics

1. R. Mir'o-Roig
2. Rosa M. Mir'o-Roig Joan Pons-Llopis
3. Emre Coskun
4. Rajesh S. Kulkarni
5. G. Casnati
6. Yusuf Mustopa

In Geometry and Topology

1. G. Casnati
2. Rosa M. Mir'o-Roig Joan Pons-Llopis
3. R. Mir'o-Roig
4. J. Pons-Llopis
5. Emre Coskun
6. Rajesh S. Kulkarni
7. Yusuf Mustopa
8. L. Costa

Citations in the corpus

• n-dimensional Fano varieties of wild representation type (2010, methodology): “We refer to [16,4,5] for more details on Ulrich bundles.”
• THE GEOMETRY OF ULRICH BUNDLES ON DEL PEZZO SURFACES (2011, methodology): “xtend to the quadric surface case. The remainder of this section is devoted to the construction of Ulrich bundles on Xd of rank rH for 3 ≤d ≤7 and r ≥2. While this has already been done in the papers [CH],[MP2] and [CH1], we present an alternate construction based on Theorem 1.1. Proposition 3.7. Su”
• Special Ulrich bundles on non-special surfaces with $p_g=q=0$ (2016, background): “problem raised by D. Eisenbud and F.O. Schreyer in [20]. It is a wide open problem, though many scattered results are known: without any claim of completeness we recall [2], [3], [7], [8], [9], [10], [11], [12], [17], [35]. Itisofparticularinterest theexistence ofUlrich bundles ofrank2which arespeci”
• The representation type of Segre varieties (2012, background): “[7] for the case of curves and [6] for the higher dimensional case) has been proposed.”