Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.
Hilbert scheme of smooth space curves
Hilbert schemes and stable pairs: GIT and derived category wall crossings
We show that the Hilbert scheme of curves and Le Potier’s moduli space of stable pairs with one dimensional support have a common GIT construction. The two spaces correspond to chambers on either side of a wall in the space of GIT linearisations. We explain why this is not enough to prove the “DT/PT wall crossing conjecture” relating the invariants derived from these moduli spaces when the underlying variety is a 3-fold. We then give a gentle introduction to a small part of Joyce’s theory for such...
Hilbert schemes of hypersurfaces and numerical criterions.
Hilbert's Theorem 90 for K2, with Application to the Chow Groups of Rational Surfaces.