Symmetry: From Physics and Calabi-Yau Threefolds to Algebra and Gorenstein Rings

Hal Schenck ()
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Hal Schenck: Auburn University, Mathematics Department

A chapter in Nankai Symposium on Mathematical Dialogues, 2026, pp 301-309 from Springer

Abstract: Abstract We give an overview of a pair of constructions: on the geometric side, we describe Calabi-Yau manifolds, and on the algebraic side, we discuss Gorenstein rings. With certain hypotheses, Gorenstein rings give rise to Calabi-Yau manifolds [24]. Calabi-Yau manifolds are of interest for many reasons, one of which is the central role they play in physics of string theory. The first half of this note gives a brisk review of the geometry necessary to define Calabi-Yau manifolds, and the second half describes the construction of a special type of Gorenstein ring. The objects resulting from both constructions possess an internal symmetry; an open question is to find the mirror of a Calabi-Yau threefold constructed from a Gorenstein ring.

Keywords: Calabi-Yau Manifold; Gorenstein ring; Inverse system; Free resolution; Primary 14J32; Secondary 13D02 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-981-19-2328-9_35

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