A compact manifold with holonomy Spin(7) from Beauville's Calabi-Yau fourfold
Nam-Hoon Lee
TL;DR
This paper constructs a new, concrete example of a compact manifold with Spin(7) holonomy derived from Beauville's Calabi-Yau fourfold, making the complex geometry more accessible.
Contribution
It provides a explicit construction of a Spin(7) manifold from a Beauville's Calabi-Yau fourfold using products of elliptic curves with complex multiplication.
Findings
New explicit example of Spin(7) manifold
Construction method from Beauville's Calabi-Yau fourfold
Accessible approach using elliptic curves with complex multiplication
Abstract
We give a new example of a compact manifold with holonomy Spin(7) from a Beauville's Calabi-Yau fourfold. Its construction is very concrete, starting with products of elliptic curves with complex multiplications --- so probably more accessible to physicists.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry