Archivio Istituzionale della RicercaWe extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.
Horrocks Correspondence on a Quadric Surface / Malaspina, Francesco; A. P., Rao. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 169:1(2014), pp. 15-31. [10.1007/s10711-013-9839-0]
Horrocks Correspondence on a Quadric Surface
MALASPINA, FRANCESCO;
2014
Abstract
We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines, which includes the first cohomology module of the bundle, and prove that there is a one to one correspondence between these sets of invariants and isomorphism classes of vector bundles without line bundle summands.
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https://hdl.handle.net/11583/2513748
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