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arXiv · 1401.6549

Noncommutative Grassmannian of codimension two has coherent coordinate ring

Dmitri Piontkovski
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Abstract

A noncommutative Grassmannian NGr(m, n) is introduced by Efimov, Luntz, and Orlov in `Deformation theory of objects in homotopy and derived categories III: Abelian categories' as a noncommutative algebra associated to an exceptional collection of n-m+1 coherent sheaves on P^n. It is a graded Calabi--Yau Z-algebra of dimension n-m+1. We show that this algebra is coherent provided that the codimension d = n-m of the Grassmannian is two. According to op. cit., this gives a t-structure on the derived category of the coherent sheaves on the noncommutative Grassmannian. The proof is quite different from the recent proofs of the coherence of some graded 3-dimensional Calabi--Yau algebras and is based on properties of a PBW-basis of the algebra.

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Dmitri Piontkovski. 2022-09-18. Noncommutative Grassmannian of codimension two has coherent coordinate ring. https://arxiv.org/abs/1401.6549

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