Rank 2 stable vector bundles on \({\mathbb{P}}^ 3({\mathbb{C}})\) with Chern classes \(c_ 1=-1,\) \(c_ 2=4\)
In this paper one shows that the moduli space M(-1,4) of stable rank 2 vector bundles on \({\mathbb{P}}^ 3\) with \(c_ 1=-1\), \(c_ 2=4\) has two connected components, corresponding to the two possible spectra: (-2,- 1,0,1),(-1,-1,0,0). Both of them are quasiprojective, irreducible, rational (of dimensions 27 and 28). The first is smooth, the other is showed to be generically smooth (the authors do not know whether it is also everywhere smooth). The method is to study the curves which are zero-sets of sections of E(t), E in M(-1,4), with t minimal. The paragraph 5 is probably of interest in itself, where an insight into the classification of curves of degree 6 (with nilpotents) is given.
scientific article; zbMATH DE number 3902807
scientific article