Effective adjunction theory

  • Marco Andreatta
  • Claudio Fontanari


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 \(H^0(X, m_0K_X+H)=0\) for some \(m_0=m_0(H)>0\). Let X be a projective 4-fold, L an ample divisor and t an integer with \(t \ge 3\). If \(K_X+tL\) is pseudo-effective, then \(H^0(X, K_X+tL) \ne 0\).


Termination of adjunction Uniruledness Quasi polarized pair Minimal model program Canonical singularities 

Mathematics Subject Classification

14E30 14J40 14J35 14N30 


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Copyright information

© Università degli Studi di Ferrara 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di TrentoTrentoItaly

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