Extension theorems, non-vanishing and the existence of good minimal models

By J. Demailly, Christopher D. Hacon, Mihai Paun. 2010

98 citations recorded by the source corpus.

We prove an extension theorem for effective purely log-terminal pairs (X, S + B) of non-negative Kodaira dimension $${\kappa (K_X+S+B)\ge 0}$$ . The main new ingredient is a refinement of the Ohsawa–Takegoshi L2 extension theorem involving singular Hermitian metrics.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ff06b60d6600846a39759248679af09c9bd184d8

How researchers see this paper

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In Applied Mathematics

1. Hiromu Tanaka
2. Paolo Cascini
3. Christopher D. Hacon
4. C. Birkar

In Geometry and Topology

1. Paolo Cascini
2. Hiromu Tanaka
3. C. Birkar
4. Christopher D. Hacon
5. O. Fujino
6. Chi Li
7. J. Witaszek
8. J. Waldron

Citations in the corpus

• An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (2013, unknown): “ted by taking the limit of suitable metrics hm. For example, this strategy plays a crucial role in the proofof the invariance of plurigenera or the extension theorem for pluri-canonical sections (see [DHP13], [Pa˘u07], [Siu98]). However it seems to be quite hard to investigate the regularity (smooth”
• Purely Log Terminal Threefolds with Non-Normal Centres in Characteristic Two (2016, methodology): “Using the same construction as in the proof of Theorem 1.1, we produce a plt pair such that the restriction maps for the log pluri-canonical divisors are not surjective, contrary to what happens in characteristic zero (cf. [HM07, Theorem 5.4.21], [DHP13, Corollary 1.8]): Theorem 1.2.”