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Deformations over non-commutative base

Yujiro Kawamata

Abstract

We make some remarks on deformations over non-commutative base. We describe the base algebra of versal deformations using $T^1$ and $T^2$.

Deformations over non-commutative base

Abstract

We make some remarks on deformations over non-commutative base. We describe the base algebra of versal deformations using and .
Paper Structure (4 sections, 3 theorems, 34 equations)

This paper contains 4 sections, 3 theorems, 34 equations.

Table of Contents

  1. multi-pointed non-commutative deformations
  2. convergence and moduli
  3. flopping contractions of $3$-folds
  4. abstract description using $T^1$ and $T^2$

Key Result

Proposition 2.1

Let $V \cong k^n$ with coordinate linear functions $x_1,\dots,x_n$, and let $W \cong k^m$ be defined by $x_{m+1} = \dots = x_n = 0$. Then the formal semi-universal NC deformation of $W$ as a linear subspace of $V$ has the parameter algebra $\hat{R}$ and the ideal $\hat{I}$ given as follows:

Theorems & Definitions (8)

  • Remark 1.1
  • Proposition 2.1
  • proof
  • Example 2.2
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof