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Smooth Euler-symmetric varieties generated by a single polynomial

Cong Ding, Zhijun Luo

Abstract

We classify smooth Euler-symmetric varieties corresponding to the symbol system generated by a single reduced polynomial.

Smooth Euler-symmetric varieties generated by a single polynomial

Abstract

We classify smooth Euler-symmetric varieties corresponding to the symbol system generated by a single reduced polynomial.
Paper Structure (4 sections, 19 theorems, 51 equations)

This paper contains 4 sections, 19 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. EKP-Homaloidal polynomials and smoothness of Euler-symmetric varieties
  3. Białynicki-Birula decomposition and the boundary divisor
  4. Proof of Theorem \ref{['mainthm']}

Key Result

Theorem 1.4

Let $Z \subset PV$ be a nondegenerate subvariety and let $x \in Z$ be a general point. Then the system of fundamental forms $\textbf{F}_x = \oplus_{k\geq 0}F_x^k$ is a symbol system of rank $r$ for some natural number $r\geq 1$.

Theorems & Definitions (48)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Theorem 1.4: Classical result due to E. Cartan
  • Definition 1.5
  • Theorem 1.6
  • Remark 1.7
  • Definition 1.8
  • Definition 1.9
  • Theorem 1.10
  • ...and 38 more