Toric vector bundles: GAGA and Hodge theory

Moduli of Toric Vector Bundles

We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that...

Toric Vector Bundles and Parliaments of Polytopes

We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes correspond to generators for the space of global sections and we relate edges to jets. Using the polytopes, we also exhibit toric vector bundles that are ample but not globally generated, and toric vector bundles tha...

Nonlinear Hodge equations in vector bundles

A gauge-invariant form of the nonlinear Hodge equations is studied. 1991 MSC: 58E15 (Classical field theory)

Higgs Bundles and Non-abelian Hodge Theory

Cox Rings and Pseudoeffective Cones of Projectivized Toric Vector Bundles

We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebra over the Cox ring of a blowup of a projective space along a sequence of linear subspa...