4 papers · 1 filter
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…