[Turkmath:7389] Koc Universitesi Matematik Semineri

[Kazim Buyukboduk]

MATHEMATICS SEMINAR



Date     : 23rd December, Thursday*

Time    : 16:00

Place   : SCI Z42, Science Building, Koc University


*Note the unusual day



Sefa Feza Arslan

MSGSÜ

Matematik Bölümü



“Monomial curve families supporting Rossi’s conjecture”



Rossi's conjecture saying that every Gorenstein local ring has non-decreasing

Hilbert function is not solved even for monomial curves. In [1], we show that

the Hilbert function is non-decreasing for local Gorenstein rings with embedding

dimension four associated to monomial curves, under some arithmetic assump-

tions on the generators of their de¯ning ideals in the non-complete intersection

case. In [2], by using the technique of nice gluing, we give in¯nitely many fam-

ilies of 1-dimensional local rings associated to complete intersection monomial

curves with non-decreasing Hilbert functions. In this talk, I summarize these

results and present new families of 1-dimensional local rings associated to com-

plete intersection monomial curves given with free parameters and obtained by

using not nice gluing [3].



References

[1] F. Arslan, P. Mete, Hilbert functions of Gorenstein monomial
curves, Proc. Amer.

Math. Soc. 135 (2007) 1993-2002.

[2] F. Arslan, P. Mete, M. S»ahin, Gluing and Hilbert functions of
monomial curves,

Proc. Amer. Math. Soc. 137 (2009) 2225-2232.

[3] F. Arslan, N. S»ahin, N. ÄOs Sipahi, Monomial curves obtained by
not nice gluing,

Preprint

Mimar Sinan GÄuzel Sanatlar Ä Universitesi, Matematik BÄolÄumÄu

email: feza.arslan at msgsu.edu.tr.