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

In: Nankai Symposium on Mathematical Dialogues

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  • Hal Schenck

    (Auburn University, Mathematics Department)

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.

Suggested Citation

  • Hal Schenck, 2026. "Symmetry: From Physics and Calabi-Yau Threefolds to Algebra and Gorenstein Rings," Springer Books, in: Yang-Hui He & Mo-Lin Ge & Cheng-Ming Bai & Jiakang Bao & Edward Hirst (ed.), Nankai Symposium on Mathematical Dialogues, pages 301-309, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-2328-9_35
    DOI: 10.1007/978-981-19-2328-9_35
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