The Weizmann Institute of Science Faculty of Mathematics and Computer Science Seminar in Geometry and Topology Seminar Room, Room 261, Ziskind Building on Tuesday, December 6, 2011 11:00 - 12:15 Note the unusual time Michael Friedman MPI, Bonn will speak on Branch curves and adjoint curves Abstract: In 1929, Zariski found that the branch curve of a smooth cubic surface in $P^3$ (over an algebraically closed field of char=0) is a sextic plane curve with 6 cusps, all of them lying on a conic. A year later, Segre generalized this, proving a similar theorem on smooth surfaces of any degree in $P^3$. Explicitly, he proved that there are two curves of unexpectedly low degree, passing through the nodes and the cusps of the branch curve of this surface (these two curves are called adjoint curves). The generalization of these theorems to any projective smooth surface gives hope for proving Chisini's conjecture constructively: i.e. to prove that that a ramified cover of the projective plane of deg > 4 is determined by its branch curve. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>