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SUMMARY:An arithmetic count of rational plane curves - Kirsten Wickelgren\
 , Duke
DTSTART:20200219T160000Z
DTEND:20200219T170000Z
UID:TALK134392@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:A rational plane curve of degree d is a polynomial map from th
 e line to the plane of degree d. There are finitely many such curves passi
 ng through 3d-1 points\, and the number of them is independent of (generic
 ally) chosen points over the complex numbers. The problem of determining t
 hese numbers was solved by Kontsevich with a recursive formula with connec
 tions to string theory. Over the real numbers\, one can obtain a fixed num
 ber by weighting real rational curves by their Welschinger invariant\, and
  work of Solomon identifies this invariant with a local degree. It is a fe
 ature of A1-homotopy theory that analogous real and complex results can in
 dicate the presence of a common generalization\, valid over a general fiel
 d. For generically chosen points with coordinates in chosen fields\, we gi
 ve such a generalization\, providing an arithmetic count of rational plane
  curves over fields of characteristic not 2 or 3. This is joint work with 
 Jesse Kass\, Marc Levine\, and Jake Solomon.
LOCATION:MR13
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