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 < {{c_1+1}\choose 2} +1 is necessary and sufficient. For c_1^2-4c_2 > -1, 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 < 4.

Planes of matrices of constant rank and globally generated vector bundles / Boralevi, Ada; Mezzetti, Emilia. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - 65:5(2015), pp. 2069-2089. [10.5802/aif.2983]

Planes of matrices of constant rank and globally generated vector bundles

BORALEVI, ADA;
2015

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 < {{c_1+1}\choose 2} +1 is necessary and sufficient. For c_1^2-4c_2 > -1, 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 < 4.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2674266
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