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Complex hypersurface singularities and mixed singularities, an introduction
Người trình bày: GS.Mutsuo Oka, Đại học khoa học Tokyo, Nhật Bản

Địa điểm: P301A, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội
Thời gian: 09h00, ngày 3/4/2012

Abstract

For a holomorphic function with an isolated singularity at the origin, there exists well-known Milnor fibration and lots of researches has been done. A mixed function is a complex valued analytic function in variables and their conjugates . We consider the hypersurface . This is a new approach to a real algebraic variety of real codimension one. We introduce the notion of Newton non-degeneracy for mixed functions and develop a basic tool for the study of mixed hypersurface singularities. We show that there exists a canonical resolution for the hypersurface singularities defined by a mixed function . We discuss how much similarity this hypersurface has comparing with a holomorphic hypersurface. For example, we discuss Varchenko type formula for zeta functions.

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