On direct images of pluricanonical bundles

By Mihnea Cristian Popa, C. Schnell. 2014

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We show that techniques inspired by Koll\'ar and Viehweg's study of weak positivity, combined with vanishing theorems for log-canonical pairs, lead to new consequences regarding generation and vanishing properties for direct images of pluricanonical bundles. We formulate the strongest such results as Fujita conjecture-type statements, which are then shown to govern a range of fundamental properties of direct images of pluricanonical and pluriadjoint line bundles, like effective vanishing theorems, weak positivity, or generic vanishing.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d67d618e20f55725d6c4b8f03d398a47ab98bfdd

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun (2016, background): “s a direct summand of ϕ ∗ωZ. Applying Koll´ar vanishing, Theorem 8.1, we deduce that Hi(A,hb ∗ω ⊗m X1 ⊗L⊗d) = 0 for all i>0 and all d≥ (g+ m)(m−1) + 1, which ﬁnishes the proof. (The main result of [PS14] shows that one can in fact take d≥ m(g+ 1) −g.) Proposition 8.2. Let f: X→ Y be a morphism of”