Numerically positive line bundles on a complex projective smooth algebraic surface S are studied. In particular, for any such line bundle L \in Pic(S) we prove the following facts: (i) g(L) \geq 0 and (ii) L is a mple if g(L) \leq 1, g standing for the arithmetic genus. Some applications are discussed. We also investigate numerically positive non-ample line bundles L with g(L)=2.
Numerically positive divisors on algebraic surfaces / A. Lanteri, B. Rondena. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - 53:2(1994), pp. 145-154. [10.1007/BF01264018]
Numerically positive divisors on algebraic surfaces
A. LanteriPrimo
;
1994
Abstract
Numerically positive line bundles on a complex projective smooth algebraic surface S are studied. In particular, for any such line bundle L \in Pic(S) we prove the following facts: (i) g(L) \geq 0 and (ii) L is a mple if g(L) \leq 1, g standing for the arithmetic genus. Some applications are discussed. We also investigate numerically positive non-ample line bundles L with g(L)=2.
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