Title: An arithmetic count of rational plane curves

Abstract: There are finitely many degree d rational plane curves passing through 3d-1
points, and over the complex numbers, this number is independent of
(generically) chosen points. For example, there are 12 degree 3 rational
curves through 8 points, one conic passing through 5, and one line passing
through 2. Over the real numbers, one can obtain a fixed number by weighting
real rational curves by their Welschinger invariant, and work of Solomon
identifies this invariant with a local degree. It is a feature of
A1-homotopy theory that analogous real and complex results can indicate the
presence of a common generalization, valid over a general field. We develop
and compute an A1-degree, following Morel, of the evaluation map on
Kontsevich moduli space to obtain an arithmetic count of rational plane
curves, which is valid for any field k of characteristic not 2 or 3. This
shows independence of the count on the choice of generically chosen points
with fixed residue fields, strengthening a count of Marc Levine. This is
joint work with Jesse Kass, Marc Levine, and Jake Solomon.