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.

Planes of matrices of constant rank and globally generated vector bundles / Boralevi, Ada; Mezzetti, E.. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 0373-0956. - 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\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.
65
5
2069
2089
10.5802/aif.2983
http://aif.cedram.org/cedram-bin/article/AIF_2015__65_5_2069_0.pdf
https://arxiv.org/abs/1402.2167
Boralevi, Ada; Mezzetti, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/32462
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