Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A note on the Gromov width of toric manifolds

Narasimha Chary Bonala, Stéphanie Cupit-Foutou

Abstract

The Gromov width of a uniruled projective Kähler manifold can be bounded from above by the symplectic area of its minimal curves. We apply this result to toric varieties and thus get in this case upper bounds expressed in toric combinatorial invariants.

A note on the Gromov width of toric manifolds

Abstract

The Gromov width of a uniruled projective Kähler manifold can be bounded from above by the symplectic area of its minimal curves. We apply this result to toric varieties and thus get in this case upper bounds expressed in toric combinatorial invariants.
Paper Structure (14 sections, 19 theorems, 41 equations)

This paper contains 14 sections, 19 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Upper bounds for the Gromov width of Kähler manifolds
  3. Gromov's Theorem
  4. Minimal curves
  5. Proof of Theorem \ref{['thm:main1']}
  6. Upper bounds for the Gromov width of toric varieties
  7. Free curves on toric varieties
  8. Minimal curves on toric varieties
  9. Proof of Theorem \ref{['thm:toric']}
  10. Comparison with previous results
  11. Lu's results in Lu06a
  12. Some questions raised in HLS
  13. Conjecture 3.12 in AHN
  14. Seshadri constants

Key Result

Theorem 1.1

Let $X$ be a projective complex manifold and $\omega$ a Kähler form of $X$. For any minimal curve $C$ of $X$, we have the inequality

Theorems & Definitions (30)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 2.1: Gromov
  • Theorem 2.2: Kol
  • Theorem 2.3
  • Lemma 2.4
  • proof
  • Theorem 2.5: Kol
  • Lemma 2.6
  • proof
  • ...and 20 more