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F-blowups of normal surface singularities

Nobuo Hara, Tadakazu Sawada, Takehiko Yasuda

Abstract

We study F-blowups of non-F-regular normal surface singularities. Especially the cases of rational double points and simple elliptic singularities are treated in detail.

F-blowups of normal surface singularities

Abstract

We study F-blowups of non-F-regular normal surface singularities. Especially the cases of rational double points and simple elliptic singularities are treated in detail.

Paper Structure

This paper contains 15 sections, 21 theorems, 78 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Blowups at modules
  4. F-blowups
  5. Computing the Frobenius pushforward
  6. The case of a polynomial ring
  7. The general case
  8. Implementation to Macaulay2
  9. Computing the singular and non-normal loci of a blowup
  10. Embedding F-blowups into the Grassmannian and the projective space
  11. F-blowups of rational surface singularities
  12. $D_{2n}^0$-singularities.
  13. F-blowups of simple elliptic singularities
  14. The F-pure case.
  15. The non-F-pure case.

Key Result

Proposition 2.4

The blowup at ${\mathcal{M}}$ is isomorphic to the blowup at $\mathcal{I}_{{\mathcal{M}}}$,

Theorems & Definitions (46)

  • Definition 2.1
  • Example 2.2
  • Example 2.3
  • Proposition 2.4: See OZVi
  • Proposition 2.5: Vi
  • Definition 2.6: Y1
  • Lemma 2.7
  • Proposition 2.8
  • Proposition 2.9
  • Lemma 3.1: H
  • ...and 36 more