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Fano varieties with split tangent sheaf

Andreas Höring

Abstract

Let $X$ be a mildly singular Fano variety such that the tangent sheaf is a direct sum. We show that the direct factors are algebraically integrable, so the infinitesimal decomposition induces a product structure on a quasi-étale cover of $X$.

Fano varieties with split tangent sheaf

Abstract

Let be a mildly singular Fano variety such that the tangent sheaf is a direct sum. We show that the direct factors are algebraically integrable, so the infinitesimal decomposition induces a product structure on a quasi-étale cover of .
Paper Structure (10 sections, 80 equations)

This paper contains 10 sections, 80 equations.

Table of Contents

  1. Introduction
  2. Main result
  3. Background and strategy of proof
  4. Notation and basic facts
  5. Reflexive sheaves and distributions
  6. First Chern class and split tangent sheaf
  7. Fibrations on varieties with split tangent sheaf
  8. Relative tangent sheaf
  9. Descent of the splitting
  10. Proofs of the main results

Theorems & Definitions (16)

  • proof
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  • proof
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  • ...and 6 more