# Resolving singularities of curves with one toric morphism

@inproceedings{Felipe2021ResolvingSO, title={Resolving singularities of curves with one toric morphism}, author={A. B. de Felipe and Pedro D. Gonz'alez P'erez and Hussein Mourtada}, year={2021} }

We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in terms of a sequence of maximal contact curves associated to C. We prove that there exists a toric modification, after reembedding, which provides an embedded resolution of C. We use properties of the…

## References

SHOWING 1-10 OF 45 REFERENCES

Resolving Singularities of Plane Analytic Branches with one Toric Morphism

- Mathematics
- 2000

Let (C, 0) be an irreducible germ of complex plane curve. Let Γ ⊂ ℕ be the semigroup associated to it and C Γ ⊂ ℂ g+1 the corresponding monomial curve, where g is the number of Puiseux exponents of…

Jet schemes and minimal embedded desingularization of plane branches

- Mathematics
- 2013

For a plane branch C with g Puiseux pairs, we determine the irreducible components of its jet schemes which correspond to the star (or rupture) and end divisors that appear on the dual graph of the…

Approximate roots, toric resolutions and deformations of a plane branch

- Mathematics
- 2008

We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of…

Invariants of singularities, generating sequences and toroidal structures

- Mathematics
- 2019

Over the last few decades, multiplier ideals and their associated jumping numbers have become an important topic in the field of birational geometry of complex algebraic varieties and in singularity…

Torical modification of Newton non-degenerate ideals

- Mathematics
- 2012

We give a definition of Newton non-degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non-degeneracy to varieties that are not…

Toric embedded resolutions of quasi-ordinary hypersurface singularities

- Mathematics
- 2003

A germ of a complex analytic variety is quasi-ordinary if there exists a finite projection to the complex affine space with discriminant locus contained in a normal crossing divisor. Some properties…

Multiplier ideals of plane curve singularities via Newton polygons

- Mathematics
- 2021

We give an effective method to determine the multiplier ideals and jumping numbers associated with a curve singularity C in a smooth surface. We characterize the multiplier ideals in terms of certain…

Local tropicalizations of splice type surface singularities

- Mathematics
- 2021

Splice type surface singularities were introduced by Neumann and Wahl as a generalization of the class of Pham-Brieskorn-Hamm complete intersections of dimension two. Their construction depends on a…

The arc space of a toric variety

- Mathematics
- 2003

Abstract The Nash problem on arc families is affirmatively answered for a toric variety by Ishii and Kollar's paper which also shows the negative answer for general case. The Nash problem is one of…

Compactifications of subvarieties of tori

- Mathematics
- 2004

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice…