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.
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yaeli Malka   <yaeli.malka@weizmann.ac.il>