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Failure of the Hasse Principle on General K3 Surfaces
We show that transcendental elements of the Brauer group of an algebraic surface can obstruct the Hasse principle. We construct a general K3 surface X of degree 2 over Q, together with a two-torsion Brauer class that is ...
Effective Computation of Picard Groups and Brauer-Manin Obstructions of Degree Two K3 Surfaces Over Number Fields
Using the Kuga-Satake correspondence we provide an effective algorithm for the computation of the Picard and Brauer groups of K3 surfaces of degree 2 over number fields.
Log minimal model program for the moduli space of stable curves: the first flip
We give a geometric invariant theory (GIT) construction of the log canonical model M¯g(α) of the pairs (M¯g,αδ) for α∈(7/10–ϵ,7/10] for small ϵ∈Q+. We show that M¯g(7/10) is isomorphic to the GIT quotient of the Chow variety ...