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Transactions of the American Mathematical Society

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On polarized surfaces $(X,L)$ with $h^{0}(L)>0$, $\kappa (X)=2$,
and $g(L)=q(X)$


Author: Yoshiaki Fukuma
Journal: Trans. Amer. Math. Soc. 348 (1996), 4185-4197
MSC (1991): Primary 14C20; Secondary 14J29
DOI: https://doi.org/10.1090/S0002-9947-96-01705-9
MathSciNet review: 1370640
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Abstract: Let $X$ be a smooth projective surface over $\mathbb {C}$ and $L$ an ample Cartier divisor on $X$. If the Kodaira dimension $\kappa (X)\leq 1$ or $\operatorname {dim}H^{0}(L)>0$, the author proved $g(L)\geq q(X)$, where $q(X)=\operatorname {dim}H^{1}(\mathcal {O}_{X})$. If $\kappa (X)\leq 1$, then the author studied $(X,L)$ with $g(L)=q(X)$. In this paper, we study the polarized surface $(X,L)$ with $\kappa (X)=2$, $g(L)=q(X)$, and $\operatorname {dim}H^{0}(L)>0$.


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Additional Information

Yoshiaki Fukuma
Affiliation: Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
Email: fukuma@math.titech.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-96-01705-9
Keywords: Projective algebraic surface, sectional genus
Received by editor(s): June 9, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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