FB 6 Mathematik/Informatik

Institut für Mathematik

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SS 2018

17.04.2018 um 16:15 Uhr in 69/125:

Van Duc Trung (University of Genova, Italy)

The initial ideal of generic sequences and Fröberg's Conjecture

Let K be an infinite field and let I = (f1,...,fr) be an ideal in the polynomial ring R = K[x1,...,xn] generated by generic forms of degrees d1,...,dr. In the case r=n, following  an effective  method by Gao, Guan and Volny, we give a description of the initial ideal of I with respect to the degree reverse lexicographic order. From this description, we prove a conjecture stated by Pardue in 2010 under a suitable condition on d1,..., dn. This holds partial solutions to a longstanding conjecture stated by Fröberg (1985) on the Hilbert series of R/I in the case r ≤ n+2 and over an infinite field of any characteristic.