A note on non-reduced Picard schemes

Details A note on non-reduced Picard schemes A note on non-reduced Picard schemes

2008-05-07

arxiv.org/abs/0805.0848v2

J. Pure Appl. Algebra 213, 737-741 (2009)

Mathematics

Algebraic Geometry

7 pages, simplified and improved version

Scientific paper

The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques-Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension $\kappa\leq0$, that this phenomenon can be bounded for $\kappa=2$ (general type) and that it is as bad as can be in $\kappa=1$.

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