On topology of quasi-ordinary singularities

Kyungho Oh, Purdue University

Abstract

A $d$-dimensional complex analytic hypersurface germ (X,x) is quasi-ordinary if there exists a branched covering $\pi$: (X,x) $\to$ ($\doubc\sp{d}$,0) which is unbranched outside the union of coordinate hyperplanes of $\doubc\sp{d}$. Such a germ ($X,x)$ can be represented as the image of an open neighborhood of 0 in $\doubc\sp{d}$ by the map ($s\sb1,\... ,s\sb{d}) \mapsto (s\sbsp{1}{n},\... ,s\sbsp{d}{n},\zeta(s\sb1,\... ,s\sb{d})),$ n $>$ 0, where $\zeta$ is a convergent power series. The main result is that there is a spectral sequence $E\sbsp{p,q}{r}$ abutting to the homology of the link of the singularity $H\sb{p+q}(X,X - x,\doubz$). The $E\sp2$-terms of this spectral sequence can be written in terms of the Galois groups Gal (${\cal L}(\zeta\sb{i\sb0,\cdots ,i\sb{p}}) : {\cal L}\rbrack,$ where ${\cal L}$ is the quotient field of the convergent power series ring $\doubc\{t\sb1,\cdots ,t\sb{d}\}$ and $\zeta\sb{i\sb0,\cdots ,i\sb{p}}$ = $\zeta(0,\cdots ,0,t\sbsp{i\sb0}{1/n},0,\cdots ,0,t\sbsp{i\sb{p}}{1/n},0,\cdots ,0).$

Degree

Ph.D.

Advisors

Lipman, Purdue University.

Subject Area

Mathematics

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