Planes of matrices of constant rank and globally generated vector bundles

Boralevi, Ada
Mezzetti, Emilia

Publication date

January 2015

Publisher

Association des Annales de lInstitut Fourier

Abstract

We consider the problem of determining all pairs (c_1, c_2) of Chern classes of rank 2 bundles that are cokernel of a skew-symmetric matrix of linear forms in 3 variables, having constant rank 2c_1 and size 2c_1+2. We completely solve the problem in the "stable" range, i.e. for pairs with c_1^2-4c_2<0, proving that the additional condition c_2\le {{c_1+1}\choose 2} is necessary and sufficient. For c_1^2-4c_2\ge 0, we prove that there exist globally generated bundles, some even defining an embedding of P^2 in a Grassmannian, that cannot correspond to a matrix of the above type. This extends previous work on c_1\le 3

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Planes of matrices of constant rank and globally generated vector bundles

Abstract

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Planes of matrices of constant rank and globally generated vector bundles

Abstract

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