Search arXivSearch

arXiv · 1705.11156

The Łojasiewicz exponent for weighted homogeneous polynomials of two real variables

Abstract

The purpose of this paper is to give the exact value of the Łojasiewicz exponent for an isolated weighted homogeneous polynomials of two real variaibles in terms of its weights.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ould M Abderrahmane. 2017-05-31. The Łojasiewicz exponent for weighted homogeneous polynomials of two real variables. https://arxiv.org/abs/1705.11156

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

G3-Criteria and Applications

The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.

math.AG

Nodal degeneration of chiral algebras I: Global structure and gluing formula

We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.

math.AG