A Lower Bound for the Sectional Genus of Quasi-Polarized Surfaces |
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Authors: | Yoshiaki Fukuma |
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Institution: | (1) Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo, 152, Japan |
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Abstract: | Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers
and L is a nef and big divisor on X. Then we conjecture that g(L) = q(X), whereg(L) is the sectional genus of L and
. In this paper, we treat the case
. First we prove that this conjecture is true for
, and we classify (X,L) withg(L)=q(X), where
is the Kodaira dimension of X. Next we study some special cases of
. |
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Keywords: | quasi-polarized surface sectional genus |
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