Monads and regularity of vector bundles on projective varieties

Abstract

In the seventies, Horrocks showed that every vector bundle E on P2 and P3 admits a certain “double-ended resolution” by line bundles that he called monads. Monads appear in a wide variety of contexts within algebraic geometry, and they are now one of the most important tools that permit us to construct vector bundles with prescribed invariants (e.g., rank, determinant, Chern classes) and to study them with the methods of linear algebra. A large number of vector bundles on P n