/pdf/fano-bundles-over-p3-and-q3-1jjnipbfv7.pdf

Fano bundles over P3 and Q3

Multiple Structures on Smooth Support

Let M(c1, c2) be the moduli space of stable rank-2 vector bundles with Chern classes c1, c2 over the smooth quadric Q3 ⊂ ℙ4. The main result of the paper consists in a description of M(0, 2) by studying the interplay between the quadrics determined by the jumping lines and the null-correlation over the spinor variety ℙ3 = Gr (ℙ1, Q3). We describe also M(-1,2), M(-1,3) and M(0,4). The irreducibility of M(0, 4) trelies on the classification of curves Y ⊂ Q3 of degree 6 with wY = OY(−1), achieved by Manolache in the appendix.

/pdf/on-moduli-of-stable-2-bundles-with-small-chern-classes-onq3-1dy33n56jm.pdf

On moduli of stable 2-bundles with small chern classes onQ3

One classifies the globally generated vector bundles on with the first Chern class c1 = 3. The case c1 = 1 is very easy, the case c1 = 2 was done in [42], the case c1 = 3, rank =2 was settled in [21] and the case c1 ≤ 5, rank = 2 in [10]. Our work is based on Serre's theorem relating vector bundles of rank = 2 with codimension 2 lci subschemes and its generalization for higher ranks, considered firstly by Vogelaar in [48].

Constantin Bănică

Papers

Rank 2 stable vector bundles onP 3(C) with Chern classesc 1=−1,c 2=4