Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bounds on the degrees of vector fields

Marc Chardin, S. Hamid Hassanzadeh, Claudia Polini, Aron Simis, Bernd Ulrich

Abstract

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

Bounds on the degrees of vector fields

Abstract

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.
Paper Structure (7 sections, 46 theorems, 171 equations)

This paper contains 7 sections, 46 theorems, 171 equations.

Table of Contents

  1. Introduction
  2. Preliminary results and a translation from geometry to algebra
  3. The invariants
  4. Lower bounds for hypersurfaces and curves with at most planar singularities
  5. Lower bounds in terms of algebraic and geometric genus
  6. Upper bounds
  7. The Euler derivation in the module of derivation

Key Result

Proposition 1

Adopt sett-vectfield. A homogeneous $R$-linear map $\mu:H \longrightarrow R$ is induced by a vector field that leaves $X$ invariant if and only if $\mu$ can be extended to a homogeneous $R$-linear map $\nu: \Omega_k(R)\longrightarrow R$.

Theorems & Definitions (95)

  • Proposition 1
  • proof
  • Example 1
  • Proposition 2
  • proof
  • Definition 1
  • Corollary 1
  • proof
  • Remark 1
  • Proposition 3
  • ...and 85 more