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Desingularization of generic symmetric and generic skew-symmetric determinantal singularities

Sabrina Alexandra Gaube, Bernd Schober

Abstract

We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.

Desingularization of generic symmetric and generic skew-symmetric determinantal singularities

Abstract

We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
Paper Structure (4 sections, 3 theorems, 58 equations)

This paper contains 4 sections, 3 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. First Examples
  3. Proof of Theorem \ref{['Thm_1']}
  4. Proof of Theorem \ref{['Thm_2']}

Key Result

Theorem 1

Let $m, \ell \in {\mathbb{Z}}_+$ be positive integers with $2\ell \leq m$, let $R_0$ be a commutative regular ring with $\operatorname{char}(R_0) \neq 2$. The following sequence of blowing ups is an embedded resolution of singularities for the reduction of the generic skew-symmetric determinantal si where $\pi_{\alpha} \colon Z_\alpha \to Z_{\alpha- 1}$ is the blowing up with center the strict tra

Theorems & Definitions (13)

  • Theorem 1
  • Theorem 2
  • Remark 2.1
  • Example 2.2: Theorems \ref{['Thm_1']} and \ref{['Thm_2']} for $m = 2$
  • Lemma 2.3
  • proof : Proof of Lemma \ref{['Lem:Trafo']}
  • Definition 2.4
  • Example 2.5
  • Example 2.6: Theorem \ref{['Thm_2']} for $m = 3$
  • Example 2.7: Theorem \ref{['Thm_1']} for $m = 4$
  • ...and 3 more