Welschinger Signs and the Wronski Map
(New conjectured reality)


A general  real rational plane curve  C of degree d  has 3(d-2) flexes
and (d-1)(d-2)/2 complex  double points. Those double  points lying in
RP^2 are either nodes or solitary points. The Welschinger sign of C is
(-1)^s, where s is the number of solitary points. When all flexes of C
are real, its parameterization comes  from a point on the Grassmannian
under  the Wronskii  map,  and every  parameterized  curve with  those
flexes is real (this is the Mukhin-Tarasov-Varchenko Theorem). Thus to
C we may associate the local degree of the Wronskii map, which is also
1 or -1. My talk will discuss work with Brazelton and McKean towards a
possible conjecture that  that these two signs associated  to C agree,
and the challenges to gathering evidence for this.