On the irregularity of cyclic coverings of the projective plane. (English) Zbl 0830.14005
Ciliberto, Ciro (ed.) et al., Classification of algebraic varieties. Algebraic geometry conference on classification of algebraic varieties, May 22-30, 1992, University of L’Aquila, L’Aquila, Italy. Providence, RI: American Mathematical Society. Contemp. Math. 162, 359-369 (1994).
Summary: We discuss the irregularity of cyclic coverings of the projective plane. We prove that if the degree \(n\) of the covering is a power of a prime number, then the irregularity is less than or equal to \((n - 1) (r - 1)/2\), where \(r\) is the number of the irreducible components of the branch curve. This is a generalization of an old result of O. Zariski [Proc. Natl. Acad. Sci. USA 15, 494-501 (1929)] to the case in which the branch curve is reducible. In the proof, the Alexander polynomial of the branch curve plays an important role.
For the entire collection see [Zbl 0791.00020].
For the entire collection see [Zbl 0791.00020].
MSC:
| 14E20 | Coverings in algebraic geometry |
| 14J17 | Singularities of surfaces or higher-dimensional varieties |
| 32S55 | Milnor fibration; relations with knot theory |
| 14J70 | Hypersurfaces and algebraic geometry |
