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arXiv · 2606.24606

Irreducible noncommutative quadrics

Izuru Mori·Kenta Ueyama·Wenchao Wu
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Abstract

In this paper, we study irreducible noncommutative quadrics $S/(f)$ via noncommutative graded matrix factorizations. We show that the line modules over $S/(f)$ are described by the rulings arising from indecomposable noncommutative linear matrix factorizations of $f$ of rank $2$. We study when Zhang twists of a standard smooth irreducible noncommutative quadric are standard. Finally, by identifying all singular central Sklyanin quadrics, we prove that every smooth central Sklyanin quadric is standard.

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Izuru Mori, Kenta Ueyama, Wenchao Wu. 2026-06-23. Irreducible noncommutative quadrics. https://arxiv.org/abs/2606.24606

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