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In the approach, the on-shell scattering process "tree" is described by a positive Grassmannian, a structure in algebraic geometry analogous to a convex polytope, that generalizes the idea of a simplex in projective space.
For finite projective spaces of geometric dimension at least three, Wedderburn's little theorem implies that the division ring over which the projective space is defined must be a finite field, GF(q), whose order (that is, number of elements) is q (a prime power).
The theorem for compact Riemann surfaces can be deduced from the algebraic version using Chow's theorem and the GAGA principle: in fact, every compact Riemann surface is defined by algebraic equations in some complex projective space.
a Scorza variety of dimension n in projective space of dimension 3n/2 + 2 that can be isomorphically projected to a hyperplane.
a variety contained in a Hilbert scheme that parametrizes curves in projective space with given degree, arithmetic genus, and number of nodes and no other singularities.