Universität Konstanz Fachbereich Mathematik und Statistik Schwerpunkt Reelle Geometrie und Algebra Einladung Im Oberseminar Reelle Geometrie und Algebra hält Rainer Sinn (Georgia Institute of Technology) am Freitag, 10.06.2016, einen Vortrag zum Thema: Low-rank sum-of-squares representations on varieties of minimal degree Der Vortrag findet um 13:30 Uhr in F426 statt. Alle Interessenten sind herzlich eingeladen. Abstract: We will give a quantitative proof of the result that every nonnegative quadratic form on a variety X of minimal degree is a sum of dim(X)+1 squares of linear forms in the homogeneous coordinate ring of X. Our proof works the same for all varieties of minimal degree and recovers the bounds that were proved with different methods. The proof also shows that there are only finitely many representations of a general nonnegative quadratic form as a sum of dim(X)+1 squares. We will count the number of representations on all 2-dimensional rational normal scrolls, completing the picture for all surfaces of minimal degree with the results on ternary quartics by Powers, Reznick, Scheiderer, Sottile. Interestingly, smooth quadratic forms on rational normal scrolls might have different numbers of representations: we need stronger assumptions on the generic forms to obtain the general number of representations. Sebastian Gruler Koordinator Oberseminar
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