Shokurov's ACC conjecture for log canonical thresholds on smooth varieties

By Tommaso de Fernex, L. Ein, M. Mustaţă. 2009

82 citations recorded by the source corpus.

Shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition. In this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties and, more generally, on locally complete intersection varieties and on varieties with quotient singularities.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/814d3c4d7ad4a6caa045237ca12329d9ae4132e3

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In Geometry and Topology

1. Qi’an Guan
2. Xiangyu Zhou
3. J. McKernan
4. Christopher D. Hacon
5. M. Mustaţă
6. Chi Li
7. C. Birkar
8. H. Blum

In Mathematical Physics

1. J. McKernan
2. Qi’an Guan
3. Christopher D. Hacon
4. M. Mustaţă
5. Xiangyu Zhou
6. C. Birkar
7. J. Kollár
8. H. Blum

Citations in the corpus

• ACC for log canonical thresholds (2012, result): “ and [21]. When the dimension is three, [19] proves that 1 is not an accumulation point from below and (1.1) follows from the results of [3]. More recently (1.1) was proved for complete intersections [9] and even when Xbelongs to a bounded family, [10]. The log canonical threshold is an interesting ”
• Effectiveness of Demailly’s strong openness conjecture and related problems (2014, methodology): “In [10], the authors proved that the above conjecture is implied by the ACC conjecture (see [36] or [28]) whose proofs can referred to [12,24] Note that c log | f | is a plurisubharmonic function, then we [21] replaced c log | f | by general plurisubharmonic functions, and obtained the following low”
• IMPANGA lecture notes on log canonical thresholds (2011, methodology): “ns out that this invariant is related in a subtle way to the log canonical threshold via reduction mod p. In Section 3 we discuss a recent joint result with T. de Fernex 4 MIRCEA MUSTAT¸A˘ and L. Ein [dFEM2], proving Shokurov’s ACC conjecture in the case of ambient smooth varieties. We do not presen”
• Existence of log canonical flips and a special LMMP (2011, unknown): “The conjecture was proved for smooth varieties by de Fernex, Ein and Mustaţă [10] who used some of the ideas of Kollár [24].”