Nash problem for a toric pair and the minimal log-discrepancy

Details Nash problem for a toric pair and the minimal log-discrepancy Nash problem for a toric pair and the minimal log-discrepancy

2010-07-29

arxiv.org/abs/1007.5244v1

Mathematics

Algebraic Geometry

6 pages, to appear in Comptes Rendus, Paris

Scientific paper

This paper formulates the Nash problem for a pair consisting of a toric variety and an invariant ideal and gives an affirmative answer to the problem. We also prove that the minimal log-discrepacy is computed by a divisor corresponding to a Nash component, if the minimal log-discrepancy is finite. On the other hand there exists a Nash component such that the corresponding divisor has negative log-discrepancy, if the minimal log-discrepancy is $-/infty$.

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