Stable vector bundles on an algebraic surface

Stable vector bundles on algebraic surfaces

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

Stable Real Algebraic Vector Bundles over a Klein Bottle

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X .

Mumford-thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface

The purpose of this paper is to study what we call the “Mumford-Thaddeus principle” which states that Geometric Invariant Theory (henceforth, “GIT”) quotients undergo specific transformations (birational and similar to Mori’s flip under some mild conditions) when the polarization (i.e. the linearized ample line bundle) is varied (cf.[MFK94], [Thaddeus93,94], and [Dolgachev-Hu93]). The case we c...

Vector bundles over algebraic curves

Canonical metrics on stable vector bundles

The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector bundles over algebraic curves via his celebrated GIT machinery. Later, in early 80’s Atiyah and Bott found an infinite dimensional symplectic quotient description of this moduli space. Since then, we...