The Picard group of a $K3$ surface and its reduction modulo $p$

Details The Picard group of a $K3$ surface and its reduction modulo $p$ The Picard group of a $K3$ surface and its reduction modulo $p$

2010-06-10

arxiv.org/abs/1006.1972v1

Mathematics

Algebraic Geometry

Scientific paper

We present a method to compute the geometric Picard rank of a $K3$ surface
over $\bbQ$. Contrary to a widely held belief, we show it is possible to verify
Picard rank $1$ using reduction only at a single prime. Our method is based on
deformation theory for invertible sheaves.

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