Let $(X,L)$ be a quasi-polarized pair, i.e. $X$ is a normal complex projective variety and $L$ is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles $K_X + rL$ for high rational numbers $r$. For this we run a Minimal Model Program with scaling relative to the divisor $K_X +rL$. We give then some applications, namely the classification up to birational equivalence of quasi-polarized pairs with sectional genus $0,1$ and of embedded projective varieties $X \subset \proj ^N$ with degree smaller than $2\codim_{\proj ^N} (X) +2$.
Minimal model program with scaling and adjunction theory
Andreatta, Marco
2013-01-01
Abstract
Let $(X,L)$ be a quasi-polarized pair, i.e. $X$ is a normal complex projective variety and $L$ is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness) of the adjoint bundles $K_X + rL$ for high rational numbers $r$. For this we run a Minimal Model Program with scaling relative to the divisor $K_X +rL$. We give then some applications, namely the classification up to birational equivalence of quasi-polarized pairs with sectional genus $0,1$ and of embedded projective varieties $X \subset \proj ^N$ with degree smaller than $2\codim_{\proj ^N} (X) +2$.File in questo prodotto:
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