The 3-cuspidal quartic and braid monodromy of degree 4 coverings. (English) Zbl 1110.14037
Ciliberto, C. (ed.) et al., Projective varieties with unexpected properties. A volume in memory of Giuseppe Veronese. Proceedings of the international conference “Varieties with unexpected properties”, Siena, Italy, June 8–13, 2004. Berlin: Walter de Gruyter (ISBN 3-11-018160-6/hbk). 113-129 (2005).
The authors study certain deformations of bidouble Galois covers of the product of two complex projective lines in connection with examples of simply connected algebraic surfaces which are diffeomorphic but not deformation equivalent. The discriminant surface of the deformation space is shown to be a quartic hypersurface isomorphic to the discriminant of the space of degree three polynomials on the projective line. Several nice properties of this hypersurface are established. The local braid monodromy of the deformed degree four coverings is determined. The local deformed branch curves that appear are the classical three-cuspidal plane quartics with a bitangent at infinity.
For the entire collection see [Zbl 1089.14001].
For the entire collection see [Zbl 1089.14001].
Reviewer: Daniel Matei (Bucureşti)
MSC:
| 14J80 | Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) |
| 14N25 | Varieties of low degree |
| 57M12 | Low-dimensional topology of special (e.g., branched) coverings |
| 58K15 | Topological properties of mappings on manifolds |
| 32S50 | Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants |
| 14E20 | Coverings in algebraic geometry |
