4 research outputs found
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.