Geometriae Dedicata

, Volume 64, Issue 2, pp 229–251

A Lower Bound for the Sectional Genus of Quasi-Polarized Surfaces

  • Yoshiaki Fukuma

DOI: 10.1023/A:1004939700290

Cite this article as:
Fukuma, Y. Geometriae Dedicata (1997) 64: 229. doi:10.1023/A:1004939700290


Let (X,L) be a quasi-polarized variety, i.e. X is a smooth projective variety over the complex numbers \(\mathbb{C}\) 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 \(q(X) = \dim H^1 (\mathcal{O}_X )\). In this paper, we treat the case \(\dim X = 2\). First we prove that this conjecture is true for \(\kappa (X) \leqslant 1\), and we classify (X,L) withg(L)=q(X), where \(\kappa (X)\) is the Kodaira dimension of X. Next we study some special cases of\(\kappa (X) = 2\).

quasi-polarized surface sectional genus 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Yoshiaki Fukuma
    • 1
  1. 1.Department of MathematicsTokyo Institute of TechnologyOh-Okayama, Meguro-ku, TokyoJapan

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