On the Hitchin morphism for higher-dimensional varieties

Near weights on higher dimensional varieties

We generalize the concept of near weight stated in [2007, IEEE Trans. Inform. Theory 53(5), 1919–1924] in the sense that we consider maps to arbitrary wellordered semigroups instead of the nonnegative integers. This concept can be used as a tool to study AG codes based on more than one point via elementary methods only.

Codes from Higher - Dimensional Varieties

A Splitting Criterion for Vector Bundles on Higher Dimensional Varieties

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on arbitrary smooth complex projective varieties of dimension ≥ 4, which asserts that a vector bundle E on X splits iff its restriction E|Y to an ample smooth codimension 1 subvariety Y ⊂ X splits.

Splitting Criteria for Vector Bundles on Higher Dimensional Varieties

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension ≥ 4, over which every extension of line bundles splits.

On the Birational Unboundedness of Higher Dimensional Q-fano Varieties

We show that the family of (Q-factorial and log terminal) Q-Fano n-folds with Picard number one is birationally unbounded for n ≥ 6.