Browsing by Author "Arslan, F."
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Item Open Access A fast algorithm for constructing Arf closure and a conjecture(Academic Press, 2014) Arslan, F.; Şahin, N.In this article, we give a fast and an easily implementable algorithm for computing the Arf closure of an irreducible algebroid curve (or a branch). Moreover, we study the relation between the branches having the same Arf closure and their regularity indices. We give some results and a conjecture, which are steps towards the interpretation of Arf closure as a specific way of taming the singularity.Item Open Access Genus calculations of complete intersections(Taylor & Francis Inc., 1998) Arslan, F.; Sertöz, S.Item Open Access On the Cohen–Macaulayness of tangent cones of monomial curves in A 4 (K)(TÜBİTAK, 2019-05) Arslan, F.; Katsabekis, Anargyros; Nalbandıyan, M.In this paper we give necessary and sufficient conditions for the Cohen–Macaulayness of the tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the case where C is a Gorenstein noncomplete intersection monomial curve and we generalize some results in the literature. Moreover, by using these results, we construct families supporting Rossi’s conjecture, which is still open for monomial curves in 4-dimensional affine space.