Math seminar at SISSA

[Emanuele Tuillier Illingworth]

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SISSA GEOMETRY AND MATH PHYS  SEMINARS
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Dr. Luca Benzo (Roma Due, benzo at axp.mat.uniroma2.it) will give a talk on

Linear systems containing the general curve of genus g

on Thursday, June 28th, at 14:30 pm in Room 136 (SISSA Building A).

Abstract: Let \bar M_g and \bar M_g,n be respectively the (coarse)
moduli space of stable and n-pointed stable complex curves of genus g.
It is a well-known fact that for g>= 3 the uniruledness of \bar M_g is
equivalent to the existence of a surface S which is not irrational
ruled carrying a positive-dimensional linear system containing the
general curve of genus g.
It will be shown how to use linear systems of this kind to construct
rational curves on some \bar M_g,n passing through the general point,
hence proving their uniruledness. The argument uses Brill-Noether
theory and characteristic linear series.
In the end the existence of linear systems containing the general
curve of genus g on complete intersection surfaces will be discussed.