Inflectional loci of scrolls over smooth, projective varieties

Discriminant Loci of Varieties with Smooth Normalization

Homogeneous projective bundles over abelian varieties

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of commutative group schemes; the irreducible bundles correspond to Heisenberg groups and their standard representations. Our results extend those of Mukai on semi-homo...

Groups of Autoequivalences of Derived Categories of Smooth Projective Varieties

On Varieties of Almost Minimal Degree I : Secant Loci of Rational Normal Scrolls

To provide a geometrical description of the classification theory and the structure theory of varieties of almost minimal degree, that is of non-degenerate irreducible projective varieties whose degree exceeds the codimension by precisely 2, a natural approach is to investigate simple projections of varieties of minimal degree. Let X̃ ⊂ P K be a variety of minimal degree and of codimension at le...

Non-finiteness Properties of Fundamental Groups of Smooth Projective Varieties

For each integer n ≥ 2, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n + 1 and whose universal cover is a Stein manifold, homotopy equivalent to an infinite bouquet of n-dimensional spheres. This non-finiteness phenomenon is also reflected in the fact that the homotopy group πn(M), viewed as...