• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

Noncommutative Grassmannian of codimension two has coherent coordinate ring

arxiv.org. math. Cornell University, 2014. No.  arXiv:1401.6549.
A noncommutative Grassmanian 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 Grassmanian is two. According to op. cit., this gives a t-structure on the derived category of the coherent sheaves on the noncommutative Grassmanian. 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.