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Calabi--Yau complete intersections in exceptional Grassmannians

Atsushi Ito, Makoto Miura, Shinnosuke Okawa, Kazushi Ueda

Abstract

We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we find a new family of Calabi--Yau 3-folds in an $E_6$-Grassmannian.

Calabi--Yau complete intersections in exceptional Grassmannians

Abstract

We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we find a new family of Calabi--Yau 3-folds in an -Grassmannian.

Paper Structure

This paper contains 4 sections, 5 theorems, 47 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Equivariant vector bundles over G/P
  3. Complete Intersections of Equivariant Vector Bundles
  4. Rational homogeneous spaces of exceptional types

Key Result

Theorem 1.1

A complete intersection Calabi--Yau 3-fold of a globally generated completely reducible equivariant vector bundle $\mathcal{E}$ on an exceptional Grassmannian $G/P$, which is not a complete intersection of line bundles on a projective space, is one of those appearing in tb:CY3.

Theorems & Definitions (6)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1: cf. e.g. MR1038279
  • proof : Sketch of proof
  • Lemma 3.1: cf. e.g. MR1038279