Secant Spaces and Syzygies of Special Line Bundles on Curves
Marian Aprodu (Bucharest, z.Z. MPI)  Seminar Algebraic Geometry (SAG)
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When 
Jul 17, 2014 from 10:30 am to 11:30 am 
Where  Bonn, Hörsaal MPI, Vivatsgasse 7 
Contact Name  Sachinidis 
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This is a joint work with Edoardo Sernesi. We study syzygies of curves embedded by special linear systems in connection with the varieties of secant planes. It is known that the existence of (p+2)secant pplanes for small p represent an obstruction for vanishing of syzygies  for example, if the curve is embedded with a 3secant line, then the ideal cannot be generated by quadrics. On the other hand, (p+2)secant pplanes always exist for larger p. We show in some cases that a nice geometric behavior of the variety of secants, seen as a subvariety in the symmetric product, is a reason for vanishing of syzygies.