A note on affine cones over Grassmannians and their stringy $E$-functions

Abstract

We compute the stringy $E$-function of the affine cone over a Grassmannian. If the Grassmannian is not a projective space then its cone does not admit a crepant resolution. Nonetheless the stringy $E$-function is sometimes a polynomial and in those cases the cone admits a noncommutative crepant resolution. This raises the question as to whether the existence of a noncommutative crepant resolution implies that the stringy $E$-function is a polynomial.

v2: final version, incorporated suggestions of the referee. To appear in Proc. Amerc. Math. Soc

References in corpus (3)

• Resolution of Stringy Singularities by Non-commutative Algebras
• Remarks on non-commutative crepant resolutions of complete intersections
• On stringy Euler characteristics of Clifford non-commutative varieties