Structure of the Newton tree at infinity of a polynomial in two variables

Autor:	Cassou-Nogues, Pierrette, Daigle, Daniel
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Geometry 14R10 14H45 14H50 (Primary)
Druh dokumentu:	Working Paper
Popis:	Let $f:\mathbb{C}^2 \to \mathbb{C}$ be a polynomial map. Let $\mathbb{C}^2 \subset X$ be a compactification of $\mathbb{C}^2$ where $X$ is a smooth rational compact surface and such that there exists a morphism of varieties $\Phi :X\to \mathbb{P}^1$ which extends $f$. Put $\mathcal{D}=X\setminus \mathbb{C}^2$; $\mathcal{D}$ is a curve whose irreducible components are smooth rational compact curves and all its singularities are ordinary double points. The dual graph of $\mathcal{D}$ is a tree. We are interested in this tree, and we analyse its complexity in terms of the genus of the generic fiber of $f$. Comment: Changes from v1: we added section 7 and rewrote the introduction
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1809.02462 Zobrazit plný text záznamu View this record from Arxiv