Some examples of noncommutative projective Calabi-Yau schemes
Yuki Mizuno
TL;DR
This paper constructs new examples of noncommutative projective Calabi-Yau schemes using noncommutative Segre products and quantum hypersurfaces, and compares them with classical counterparts and existing examples.
Contribution
It introduces novel constructions of noncommutative Calabi-Yau schemes and demonstrates their distinctness from known commutative examples.
Findings
Some constructions are essentially new examples of noncommutative projective Calabi-Yau schemes.
Comparison with commutative Calabi-Yau varieties and existing noncommutative examples.
Highlights the potential richness of noncommutative geometry in Calabi-Yau contexts.
Abstract
In this article, we construct some examples of noncommutative projective Calabi-Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare them with commutative Calabi-Yau varieties and examples by Kanazawa. In particular, we show that some of our constructions are essentially new examples of noncommutative projective Calabi-Yau schemes.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons