Gavril Farkas,
Brill-Noether loci and the gonality stratification of the moduli
space of curves
Abstract: For an algebraic curve the gonality is perhaps the second most
natural invariant: it gives an
indication of how far the curve is from being rational in a way
different from what the genus
does. In this talk we consider various subvarieties of the moduli space
of curves and we study their
relative position with respect to the gonality stratification of the
moduli space of curves. We construct
smooth curves in P^r of given degree and genus and having "expected"
gonality. We apply these results
to compute certain invariants of the moduli space of curves.