# On a conjecture of Teissier: the case of log canonical thresholds

@article{Elduque2020OnAC, title={On a conjecture of Teissier: the case of log canonical thresholds}, author={Eva Elduque and Mircea Mustaţǎ}, journal={Sbornik: Mathematics}, year={2020}, volume={212}, pages={433 - 448} }

For a smooth germ of an algebraic variety and a hypersurface in , with an isolated singularity at , Teissier conjectured a lower bound for the Arnold exponent of in terms of the Arnold exponent of a hyperplane section and the invariant of the hypersurface. By building on an approach due to Loeser, we prove the conjecture in the case of log canonical thresholds. Bibliography: 21 titles.

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## References

SHOWING 1-10 OF 42 REFERENCES

Birational Geometry of Algebraic Varieties

- Mathematics
- 2010

Needless to say, tlie prototype of classification theory of varieties is tlie classical classification theory of algebraic surfaces by the Italian school, enriched by Zariski, Kodaira and others. Let…

Hodge ideals for Q-divisors, V-filtration, and minimal exponent

- Mathematics
- 2018

We explicitly compute the Hodge ideals of Q-divisors in terms of the V-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties…

Hodge ideals for Q-divisors II: V-filtration

- Mathematics
- 2018

We explicitly compute the Hodge ideals of Q-divisors in terms of the V-filtration induced by a local defining equation, inspired by a result of Saito in the reduced case. We deduce basic properties…

On Hodge spectrum and multiplier ideals

- Mathematics
- 2002

Abstract.We describe a relation between two invariants which measure the complexity of a hypersurface singularity. One is the Hodge spectrum which is related to the monodromy and the Hodge filtration…

Singularities of pairs via jet schemes

- Mathematics
- 2001

Let X be a smooth variety and Y a closed subscheme of X. By comparing motivic integrals on X and on a log resolution of (X,Y), we prove the following formula for the log canonical threshold of (X,Y):…

Formulas for multiplier ideals on singular varieties

- Mathematics
- 2004

<abstract abstract-type="TeX"><p>We prove a generalization of Demailly-Ein-Lazarsfeld's subadditivity formula and Mustaţǎ's summation formula for multiplier ideals to the case of singular varieties,…

ASYMPTOTIC HODGE STRUCTURE IN THE VANISHING COHOMOLOGY

- Mathematics
- 1982

The asymptotics of integrals which depend on a critical point of a holomorphic function and the mixed Hodge structure in the vanishing cohomology are compared. Bibliography: 38 titles.

Introduction to Singularities and Deformations

- Mathematics
- 2007

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie…

Algebraic Geometry

- MathematicsNature
- 1973

Introduction to Algebraic Geometry.By Serge Lang. Pp. xi + 260. (Addison–Wesley: Reading, Massachusetts, 1972.)