Derived autoequivalences from periodic algebras

Exceptional Sequences and Derived Autoequivalences

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y admitting a full exceptional sequence. Applications include the case in which X is Calabi-Yau and either X is a hypersurface in Y (this extends a previous result b...

Derived Autoequivalences and a Weighted Beilinson Resolution

Given a smooth (as stack) Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D(X): the first is induced by the spherical object OX , while the second is tensoring by OX(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights, is isomorph...

Groups of Autoequivalences of Derived Categories of Smooth Projective Varieties

Periodic resolutions over exterior algebras ✩

In this paper we study modules with periodic free resolutions (that is, periodic modules) over an exterior algebra. We show that any module with bounded Betti numbers (that is, a module whose syzygy modules have a bounded number of generators) must have periodic free resolution of period 2, and that for graded modules the period is 1. We also show that any module with a linear Tate resolution i...

Inductive Limit Algebras from Periodic Weighted Shifts on Fock Space

Noncommutative multivariable versions of weighted shift operators arise naturally as ‘weighted’ left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these N tuples, and then find a family of inductive limit algebras determined by the periodic weighted shifts which can be regarded as noncommutative multivariable generalizations of the Bu...