6 papers
Biliaison of sheaves
Mengyuan Zhang
We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suit…
Graded basic elements
Mengyuan Zhang
We prove the existence theorem for basic elements in the quasi-projective case, extending results of Eisenbud-Evans and Bruns from the affine case. We give several geometric applic…
Space curves on surfaces with ordinary singularities
Mengyuan Zhang
We show that smooth curves in the same biliaison class on a hypersurface in with ordinary singularities are linearly equivalent. We compute the invariants $h^0(\math…
Bundles on Pn with vanishing lower cohomologies
Mengyuan Zhang
We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli according to the Hilbe…
Free resolutions of function classes via order complexes
Justin Chen, Christopher Eur, Greg Yang +1
Function classes are collections of Boolean functions on a finite set, which are fundamental objects of study in theoretical computer science. We study algebraic properties of idea…
Lie algebras of linear systems and their automorphisms
Mengyuan Zhang
The objective of this thesis is to study the automorphism groups of the Lie algebras attached to linear systems. A linear system is a pair of vector spaces with a nondegene…