The Abhyankar-Moh theorem for plane valuations at infinity
We introduce the class of plane valuations at infinity and prove an analogue to the Abhyankar-Moh (semigroup) Theorem for it.
math.AG↗
arXiv subjects
Francisco Monserrat
Publications and source records attributed to Francisco Monserrat.
Lins Neto's examples of foliations and the Mori cone of blow-ups of $P^2$
We use a family of algebraic foliations given by A. Lins Neto to provide new evidences to a conjecture, related to the Harbourne-Hirschowitz's one and implying the Nagata's conjecture, which concerns the structure of the Mori cone of blow-ups of $\mathbb{P}^2$ at very general points.
math.AG↗
Configurations of infinitely near points
We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular foliations, and linear systems defined by clusters.
math.AG↗
The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface
For a simple complete ideal $\wp$ of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincaré series $P_{\wp}$, that gathers in an unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to $\wp$. This paper is devoted to prove that $P_{\wp}$ is a rational function giving an explicit expression for it.
math.AG↗
Fibers of pencils of curves on smooth surfaces
Let $X$ be a smooth projective surface such that linear and numerical equivalence of divisors on $X$ coincide and let $σ\subseteq |D|$ be a linear pencil on $X$ with integral general fibers. A fiber of $σ$ will be called special if either it is not integral or it has non-generic multiplicity at some of the base points (including the infinitely near ones) of the pencil. In this note we provide an algorithm to compute the integral components of the special fibers of $σ$.
math.AG↗