Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results: A projective variety X with at most canonical singularities is uniruled if and only if for each very ample Cartier divisor H on X we have H0(X,m0KX+H)=0 for some m0=m0(H)>0. Let X be a projective 4-fold, L an ample divisor and t an integer with t≥3. If KX+tL is pseudo-effective, then H0(X,KX+tL)≠0.

Effective adjunction theory / Andreatta, Marco; Fontanari, Claudio. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SCIENZE MATEMATICHE. - ISSN 1827-1510. - 64:2(2018), pp. 243-257. [10.1007/s11565-018-0300-z]

Effective adjunction theory

Marco Andreatta;Claudio Fontanari
2018-01-01

Abstract

Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results: A projective variety X with at most canonical singularities is uniruled if and only if for each very ample Cartier divisor H on X we have H0(X,m0KX+H)=0 for some m0=m0(H)>0. Let X be a projective 4-fold, L an ample divisor and t an integer with t≥3. If KX+tL is pseudo-effective, then H0(X,KX+tL)≠0.
2018
2
Andreatta, Marco; Fontanari, Claudio
Effective adjunction theory / Andreatta, Marco; Fontanari, Claudio. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SCIENZE MATEMATICHE. - ISSN 1827-1510. - 64:2(2018), pp. 243-257. [10.1007/s11565-018-0300-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/199970
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