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EnglishWe 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.
| Titolo: | Planes of matrices of constant rank and globally generated vector bundles |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/2846380 |
| URL: | http://aif.cedram.org/cedram-bin/article/AIF_2015__65_5_2069_0.pdf |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| AIF_2015__65_5_2069_0.pdf | Publisher-Version |  | Open Access Visualizza/Apri |
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