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Fibrations Over Singular K3 Surfaces and New Solutions to the Hull-Strominger System

Anna Fino, Gueo Grantcharov, Jose Medel

Abstract

Using fibrations over K3 orbisurfaces we construct new smooth solutions to the Hull-Strominger system. In particular, we prove that, for $4 \leq k \leq 22$ and $5 \leq r\leq 22$, the smooth manifolds $S^1\times \sharp_k(S^2\times S^3)$ and $\sharp_r (S^2 \times S^4) \sharp_{r+1} (S^3 \times S^3)$, have a complex structure with trivial canonical bundle and admit a solution to the Hull-Strominger system.

Fibrations Over Singular K3 Surfaces and New Solutions to the Hull-Strominger System

Abstract

Using fibrations over K3 orbisurfaces we construct new smooth solutions to the Hull-Strominger system. In particular, we prove that, for and , the smooth manifolds and , have a complex structure with trivial canonical bundle and admit a solution to the Hull-Strominger system.
Paper Structure (5 sections, 14 theorems, 65 equations, 3 tables)

This paper contains 5 sections, 14 theorems, 65 equations, 3 tables.

Table of Contents

  1. Introduction
  2. K3 orbisurfaces
  3. Construction of $T^2$-bundles over orbisurfaces
  4. Existence of Stable Bundle
  5. Proof of Theorem \ref{['theoremA']}

Key Result

Theorem 1.1

Let $4\leq k \leq 22$ and $5\leq r \leq 22$. Then the smooth manifolds $S^1 \times \sharp_{k}(S^2\times S^3)$ and $\sharp_{r}(S^2\times S^4)\sharp_{r+1} (S^3\times S^3)$ admit a complex structure with a trivial canonical bundle with a balanced metric and a solution to the Hull-Strominger system via

Theorems & Definitions (30)

  • Theorem 1.1
  • Definition 2.1
  • Definition 2.2
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • Lemma 2.3
  • Corollary 2.1
  • proof
  • Corollary 2.2
  • ...and 20 more