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- W3201979427 abstract "Let $X$ be a smooth complex projective variety of dimension $ngeq 2$ polarized by an ample line bundle $H$. For $n=2$, the structure of pairs $(X,H)$ as above is described under the assumption that $m-3dleq 4$, 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 $rleq n-2$ 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 $d:=c_{n-2}(mathcal{F})H^2$." @default.
- W3201979427 created "2021-10-11" @default.
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- W3201979427 date "2021-09-01" @default.
- W3201979427 modified "2023-10-14" @default.
- W3201979427 title "On the Structure of Generalized Polarized Manifolds with Relatively Small Second Class" @default.
- W3201979427 doi "https://doi.org/10.3836/tjm/1502179348" @default.
- W3201979427 hasPublicationYear "2021" @default.
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