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2021 On the Structure of Generalized Polarized Manifolds with Relatively Small Second Class
Antonio LANTERI, Andrea Luigi TIRONI
Tokyo J. Math. Advance Publication 1-22 (2021). DOI: 10.3836/tjm/1502179348

Abstract

Let $X$ be a smooth complex projective variety of dimension $n\geq 2$ polarized by an ample line bundle $H$. For $n=2$, the structure of pairs $(X,H)$ as above is described under the assumption that $m-3d\leq 4$, where $m$ and $d$ stand for the class and the degree of $(X,H)$, respectively. In particular, special attention is payed to the case $m-2d \leq 1$, in which $X$ turns out to be a ruled surface. In higher dimensions, adding to the above setting an ample vector bundle $\mathcal{E}$ of rank $r\leq n-2$ on $X$ such that $\mathcal{F}:=\mathcal{E}\oplus H^{\oplus (n-r-2)}$ admits a regular section vanishing on a smooth surface, by relying on the analysis made in the surface case, the structure of the generalized polarized manifold $(X,\mathcal F)$ is described for small values of $m_2-3d$, where $m_2=m_2(X,\mathcal{E},H)$ is the generalized second class defined in a previous paper and $d:=c_{n-2}(\mathcal{F})H^2$.

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Antonio LANTERI. Andrea Luigi TIRONI. "On the Structure of Generalized Polarized Manifolds with Relatively Small Second Class." Tokyo J. Math. Advance Publication 1 - 22, 2021. https://doi.org/10.3836/tjm/1502179348

Information

Published: 2021
First available in Project Euclid: 4 October 2021

Digital Object Identifier: 10.3836/tjm/1502179348

Subjects:
Primary: 14F05
Secondary: 14J26, 14J27, 14J60

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

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