Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


osu1061248740.pdf (485.37 KB)

ETD Abstract Container

Abstract Header

The link of suspension singularities and Zariski’s conjecture

Mendris, Robert
http://rave.ohiolink.edu/etdc/view?acc_num=osu1061248740

Abstract Details

2003, Doctor of Philosophy, Ohio State University, Mathematics.
This thesis is devoted to singularity theory. It is shown that some families of isolated hypersurface singularities have special and surprising properties. More precisely, we consider suspension hypersurface singularities of type g=f(x,y)+zn, where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for two pathological cases, which can be completely described. Even in the pathological cases, the link and the Milnor number of g determine uniquely the Newton pairs of f and n. One of the consequences of the result is that one recovers the equisingular type of {g=0} from its topology, in particular, (almost) all the analytic invariants of g. For such g, as a consequence, we obtain Zariski’s conjecture about the multiplicity. We also verify these results for a weighted homogeneous singularity whose link is a rational homology sphere.
Andras Nemethi (Advisor)
Mathematics
cyclic covers; links of singularities; Milnor number; Newton pairs; plane curve singularities; resolution graphs; suspension singularities; Zariski's conjecture

Recommended Citations

Citations

  • Mendris, R. (2003). The link of suspension singularities and Zariski’s conjecture [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1061248740

    APA Style (7th edition)

  • Mendris, Robert. The link of suspension singularities and Zariski’s conjecture. 2003. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1061248740.

    MLA Style (8th edition)

  • Mendris, Robert. "The link of suspension singularities and Zariski’s conjecture." Doctoral dissertation, Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1061248740

    Chicago Manual of Style (17th edition)

osu1061248740
1,576
© 2003, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.