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Some Adjunction Properties of Ample Vector Bundles

Published online by Cambridge University Press:  20 November 2018

Hironobu Ishihara*
Affiliation:
Department of Mathematics Tokyo Institute of Technology Oh-okayama, Meguro Tokyo 152-8551 Japan, email: ishihara@math.titech.ac.jp
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Abstract

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Let $\mathcal{E}$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors ${{K}_{X}}\,+\,\left( t-r \right)\,\det \,\mathcal{E}$ when $t\,\ge \,\dim\,X$ and $t\,>\,r$. As an application, we classify pairs $\left( X,\,\mathcal{E} \right)$ with ${{c}_{r}}$-sectional genus zero.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2001

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