12 research outputs found
Sums of residues on algebraic surfaces and application to coding theory
In this paper, we study residues of differential 2-forms on a smooth
algebraic surface over an arbitrary field and give several statements about
sums of residues. Afterwards, using these results we construct
algebraic-geometric codes which are an extension to surfaces of the well-known
differential codes on curves. We also study some properties of these codes and
extend to them some known properties for codes on curves.Comment: 31 page
Complete intersections: Moduli, Torelli, and good reduction
We study the arithmetic of complete intersections in projective space over
number fields. Our main results include arithmetic Torelli theorems and
versions of the Shafarevich conjecture, as proved for curves and abelian
varieties by Faltings. For example, we prove an analogue of the Shafarevich
conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.