6 papers · 1 filter
A Eudoxian study of discriminant curves associated to normal surface singularities
Evelia Rosa GarcÃa Barroso, Patrick Popescu-Pampu
Let be a finite morphism from a germ of normal complex analytic surface to the germ of at the origin. We show that the affine al…
An introduction to real oriented blowups in toric, toroidal and logarithmic geometries
Patrick Popescu-Pampu
This text is an introduction to the applications of rounding of complex log spaces (also known as Kato-Nakayama or Betti realization) to singularity theory. Log spaces in the sense…
Lotuses as computational architectures
Evelia R. GarcÃa Barroso, Pedro D. González Pérez, Patrick Popescu-Pampu
Lotuses are certain types of finite contractible simplicial complexes, obtained by identifying vertices of polygons subdivided by diagonals. As we explained in a previous paper, ea…
Approximate roots
Patrick Popescu-Pampu
Given an integral domain , a monic polynomial of degree with coefficients in and a divisor of , invertible in , there is a unique monic polynomial such…
An introduction to local tropicalization
Patrick Popescu-Pampu, Dmitry Stepanov
In this paper we explain four viewpoints on the local tropicalization of formal subgerms of toric germs, which is a local analog of the global tropicalization of subvarieties of al…
Combinatorial study of morsifications of real univariate singularities
Arnaud Bodin, Evelia Rosa GarcÃa Barroso, Patrick Popescu-Pampu +1
We study a broad class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the resulting Morse functions, via planar contac…