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Biliaison Classes of Rank Two Reflexive Sheaves on P 3
Author(s) -
Buraggina Antonella
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19992010104
Subject(s) - mathematics , rank (graph theory) , pure mathematics , cohomology , vector bundle , analogy , class (philosophy) , property (philosophy) , zero (linguistics) , space (punctuation) , chern class , projective space , algebra over a field , projective test , combinatorics , philosophy , linguistics , epistemology , artificial intelligence , computer science
A biliaison theory for rank two reflexive sheaves on projective 3 ‐ space is established, In analogy with the existing theory for curves and, more generally, for 2 ‐ codimensional subschemes of projective n ‐ space. By definition two such sheaves are in the same biliaison class if their first cohomology modules are isomorphic. A parametrization of these classes is given. It is then shown that any class not corresponding to the zero module has a structure described by the Lazarsfeld ‐ Rao property. In particular, it is shown that vector bundles are precisely the minimal elements (in the of the LR ‐ property) in their biliaison classes.