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CLASSICAL ZARISKI PAIRS

AYŞEGÜL AKYOL

Department of Mathematics, Bilkent University, 06533 Ankara, Turkey

https://doi.org/10.1142/S0218216512500915Cited by:2 (Source: Crossref)

Abstract

We enumerate and classify up to equisingular deformation all irreducible plane sextics constituting the so called classical Zariski pairs. In most cases we obtain two deformation families, called abundant and non-abundant. Four sets of singularities are realized by abundant sextics only, and one exceptional set of singularities is realized by three families, one abundant and two complex conjugate non-abundant. This exceptional set of singularities has submaximal total Milnor number 18.

Keywords:

AMSC: Primary 14H30, Secondary 14H45

References

E. Artal, J. Algebr. Geom. 3(2), 223 (1994). Web of Science, Google Scholar
A. Degtyarev, Alexander polynomial of an algebraic hypersurface, preprint LOMI, R-11-86 (1986) (in Russian) . Google Scholar
A. Degtyarev, J. Knot Theory Ramifications 3, 439 (1994). Link, Google Scholar
A. Degtyarev, J. Algebr. Geom. 17(1), 101 (2008). Crossref, Web of Science, Google Scholar
A. Degtyarev, J. London Math. Soc. 78(2), 329 (2008). Crossref, Web of Science, Google Scholar
A. Degtyarev, J. Singularities 2, 51 (2010). Crossref, Google Scholar
A. H. Durfee, Ann. Math. 232, 85 (1978). Crossref, Web of Science, Google Scholar
C. Eyral and M. Oka, J. Math. Soc. Japan 57(1), 37 (2005). Crossref, Web of Science, Google Scholar
C. F. Gauss, Disquisitiones Arithmeticae (Springer-Verlag, New York, 1986). Translated and with a preface by Arthur A. Clarke, Revised by W. C. Waterhouse, C. Greither and A. W. Grootendorst and with a preface by Waterhouse . Google Scholar
A. Libgober, Duke Math. J. 49(4), 833 (1982). Crossref, Web of Science, Google Scholar
R. Miranda and D. R. Morrison, Proc. Japan Acad. Ser. A Math. Sci. 61(10), 317 (1985). Crossref, Google Scholar
R. Miranda and D. R. Morrison, Proc. Japan Acad. Ser. A Math. Sci. 62(1), 29 (1986). Crossref, Google Scholar
V. V. Nikulin, Integer quadratic forms and some of their geometrical applications, Izv. Akad. Nauk SSSR, Ser. Mat 43 (1979) 111–177 (in Russian), Math. USSR-Izv. 43 (1980) 103–167 . Google Scholar
M. Oka and D. T. Pho, Tokyo J. Math. 25(2), 399 (2002). Crossref, Google Scholar
È. B. Vinberg, Math. USSR-Sbornik 87, 17 (1972). Google Scholar
O. Zariski, Ann. Math. 32, 485 (1931). Crossref, Google Scholar