Abstract
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.
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Ottaviani, G., Szurek, M. On moduli of stable 2-bundles with small chern classes onQ 3 . Annali di Matematica pura ed applicata 167, 191–241 (1994). https://doi.org/10.1007/BF01760334
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DOI: https://doi.org/10.1007/BF01760334