5 papers
Derived representation schemes with arbitrary coefficients and associative smoothness
Guanyu Li
We study associative smoothness through representation homology with coefficients in arbitrary finite-dimensional algebras. We prove that the higher representation homology of a fi…
Orlov's functors in Macaulay2
Michael K. Brown, Souvik Dey, Geoffrey Fatin +3
Given a commutative and graded Gorenstein ring with associated projective variety , a theorem of Orlov gives fully faithful embeddings from the graded singularity category o…
Commuting Schemes of Upper Triangular Matrices and Representation Homology
Guanyu Li
We establish a connection between generalised commuting schemes of higher genus , which are associated with a group scheme consisting of upper triangular unipot…
Computing global Ext for complexes
Michael K. Brown, Souvik Dey, Guanyu Li +1
We give a computational algorithm for computing Ext groups between bounded complexes of coherent sheaves on a projective variety, and we describe an implementation of this algorith…
A Step towards Computational Derived Algebraic Geometry: The RepHomology Package For Macaulay2
Guanyu Li
We introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representat…