Lens space surgeries and algebraic curves

I'll show that if Dehn surgery on a knot, K, yields a lens space then
K arises as the transverse intersection of an algebraic curve in C^2
with the three-sphere.  Furthermore, the genus of the piece of the
curve inside the four-ball is equal to the Seifert genus of K.  Knots
arising in this way are more general than the well-understood links of
singularities, as their singular sets may be more complicated.  The
result follows from a theorem which says that an invariant defined
using Ozsvath-Szabo theory detects when fibered knots arise from
algebraic curves with a genus constraint as above.  I will discuss
this theorem and say how the result on knots admitting lens space
surgeries follows readily from it and theorems of Ozsvath and Szabo,
and Ni, respectively.