Basics on families of hyperelliptic curves
Big Schottky.
Birational moduli and nonabelian cohomology
Birational moduli and nonabelian cohomology, II
Birational Properties of Moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces.
Bounds for the number of moduli for irregular varieties of general type.
Bridgeland-stable moduli spaces for -trivial surfaces
We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface and describe “wall-crossing behavior” for objects with the same invariants as when generates Pic and . If, in addition, is a or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover a natural...
Bubble tree compactification of moduli spaces of vector bundles on surfaces
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c 1 = 0, c 1...