Explore: Picard Schemes

→S be a morphism of schemes. The relative Picard functor (or relative Picard scheme if it is a scheme) is given by: for any S-scheme T, Pic X / S ⁡ ( T

other words it is the group of components of the Picard scheme of a variety. Its rank is called the Picard number. It is named after Francesco Severi and

atypical", as clawbacks in such schemes range from 5 percent to 30 percent, and many victims do not get anything. Picard has successfully pursued not only

13). The Albanese variety is dual to the Picard variety (the connected component of zero of the Picard scheme classifying invertible sheaves on V): Alb

Differential Galois Theory, AMS (GSM122), ISBN 978-0-8218-5318-4. Kovacic, J. J. (2005), Picard–Vessiot theory, algebraic groups and group schemes (PDF)

place by that time, with Chapter VIII already intended to cover the Picard scheme. In that letter he estimated that at the pace of writing up to that

now be explained in terms of the Picard scheme of the surface, and in particular, its failure to be a reduced scheme, which is a theme developed in Mumford's

schemes, or for quasi-projective schemes over a Noetherian ring, but it can fail in general (even for proper schemes over C), which lessens the interest

intersection number as an Euler characteristic. Let X be a scheme over a scheme S, Pic(X) the Picard group of X and G the Grothendieck group of the category

The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed