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Some results on deformations of sections of vector bundles | | Abel Castorena
; Gian Pietro Pirola
; | | Date: |
10 Oct 2015 | | Abstract: | Let $E$ be a vector bundle on a smooth complex projective variety $X$. We
study the family of sections $s_tin H^0(Eotimes L_t)$ where $L_tin Pic^0(X)$
is a family of topologically trivial line bundle and $L_0=mathcal O_X,$ that
is, we study deformations of $s=s_0$. By applying the approximation theorem of
Artin [1] we give a transversality condition that generalizes the
semi-regularity of an effective Cartier divisor. Moreover, we obtain another
proof of the Severi-Kodaira-Spencer theorem [3]. We apply our results to give a
lower bound to the continuous rank of a vector bundle as defined by Miguel
Barja [2] and a proof of a piece of the generic vanishing theorems [5] and [6]
for the canonical bundle. We extend also to higher dimension a result given in
[8] on the base locus of the paracanonical base locus for surfaces. | | Source: | arXiv, 1510.2964 | | Services: | Forum | Review | PDF | Favorites | |
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