Oberseminar
"Incoherent components of the Toric Hilbert scheme"
Rene Birkner
18.10.2009, 15:15 Uhr
Freie Universitaet Berlin
Institut fuer Mathematik
Arnimallee 3, Rm. 119
The classical Hilbert scheme is the scheme whose closed points are all subschemes of with the same Hilbert function. That is, for S=k[x0,...,xn] and an ideal I&sub#subset;S the function H(t) = (S/I)_t whose value at d is the dimension over k of the degree t part of S/I. Endowing the ring S with a multigrading, i.e. the degree of xi is ai &isin#in;, we construct the multigraded Hilbert function. This is the analogon to the classical Hilbert function with degrees in for some d > 0. Then one can consider all ideals I&sub#subset;S with the same multigraded Hilbert function, these are the closed points of the multigraded Hilbert scheme. We consider the simplest case, taking the semigroup ={&sum#sum;ni ai | ni &isin#in;} and the multigraded Hilbert function
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