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On polarized surfaces
Authors:Yoshiaki Fukuma
Affiliation:Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
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 $operatorname {dim}H^{0}(L)>0$.

Keywords:Projective algebraic surface   sectional genus
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