Singularity theory and arf rings

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2012

Öğrenci: NİL ŞAHİN

Danışman: AHMET İRFAN SEVEN

Özet:

Arf closure of a local ring corresponding to a curve branch, which carries a lot of information about the branch is an important object of study. Though both Arf rings and Arf semigroups are being studied by many mathematicians, there is not an implementable fast algorithm for constructing the Arf closure. The main aim of this thesis is to give an easily implementable fast algorithm to compute the Arf Closure of a given local ring. The speed of the algorithm is a result of the fact that the algorithm avoids computing the semigroup of the local ring. Moreover, in doing this, we give a bound for the conductor of the semigroup of the Arf Closure without computing the Arf Closure by using the theory of plane branches. We also give an exposition of plane algebroid curves and present the SINGULAR library written by us to compute the invariants of plane algebroid curves.