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Algebraic boundaries of Hilbert's SOS cones
(Cambridge University PressCompositio Mathematica, 2012-10-15)
We study the geometry underlying the difference between nonnegative
polynomials and sums of squares. The hypersurfaces that discriminate
these two cones for ternary sextics and quaternary quartics are shown
to be ...
Ample subvarieties and q-ample divisors
(ElsevierAdvances in Mathematics, 2012-03-20)
We introduce a notion of ampleness for subschemes of any codimension
using the theory of q-ample line bundles. We also investigate certain geometric
properties satisfied by ample subvarieties, e.g. the Lefschetz ...