Valuation spaces and multiplier ideals on singular varieties
By S. Boucksom, Tommaso de Fernex, C. Favre, S. Urbinati. 2013
89 citations recorded by the source corpus.
We generalize to all normal complex algebraic varieties the valuative characterization of multiplier ideals due to Boucksom-Favre-Jonsson in the smooth case. To that end, we extend the log discrepancy function to the space of all real valuations, and prove that it satisfies an adequate properness property, building upon previous work by Jonsson-Mustaţă. We next give an alternative definition of the concept of numerically Cartier divisors previously introduced by the first three authors, and prove that numerically Q-Cartier divisors coincide with Q-Cartier divisors for rational singularities. These ideas naturally lead to the notion of numerically Q-Gorenstein varieties, for which our valuative characterization of multiplier ideals takes a particularly simple form.
View Paper: https://www.semanticscholar.org/paper/8fb7a956cefc1f13a9693e805bbb7db226414131
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Citations in the corpus
- Degrees of iterates of rational maps on normal projective varieties (2017, background): “We suppose that X is numerically Q-factorial in the sense of [1].”
- Minimizing normalized volumes of valuations (2015, background): “ord o; (6) for any valuation centered at 0. Proof. To get the lower bound, we note that f2m ordo(f) m o(f)+1. So ord o(f)v(m) v(f): For the upper bound, by the way of denition of A X(v) in [JM] and [BdFU], we can assume that vis divisorial valuation with center at oby approximating the general real ”