Let E be an ample and spanned vector bundle of rank r over a complex projective surface S. It is shown that the sectional genus g(S, det E) is bounded from below by the number b = max{q(S), 2 - rchi(O(S)))} and pairs (S, E) satisfying b less-than-or-equal-to g(S, det E) less-than-or-equal-to b + 1 are characterized.
A lower bound for sectional genera of ample and spanned vector bundles on algebraic surfaces / A. Lanteri, F. Russo. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 119:4(1993), pp. 1053-1059. [10.1090/S0002-9939-1993-1176482-3]
A lower bound for sectional genera of ample and spanned vector bundles on algebraic surfaces
A. LanteriPrimo
;
1993
Abstract
Let E be an ample and spanned vector bundle of rank r over a complex projective surface S. It is shown that the sectional genus g(S, det E) is bounded from below by the number b = max{q(S), 2 - rchi(O(S)))} and pairs (S, E) satisfying b less-than-or-equal-to g(S, det E) less-than-or-equal-to b + 1 are characterized.
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