Morphisms, line bundles and moduli spaces in real algebraic geometry

Geometry of Moduli Spaces of Higgs Bundles

We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...

Morphisms of Algebraic Spaces

Birational morphisms and Poisson moduli spaces

We study birational morphisms between smooth projective surfaces that respect a given Poisson structure, with particular attention to induced birational maps between the (Poisson) moduli spaces of sheaves on those surfaces. In particular, to any birational morphism, we associate a corresponding “minimal lift” operation on sheaves of homological dimension ≤ 1, and study its properties. In partic...

MORPHISMS OF ALGEBRAIC SPACES Contents

MORPHISMS OF ALGEBRAIC SPACES Contents