BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kirsten Wickelgren (Duke University\, North Carolina) DTSTART:20210114T140000Z DTEND:20210114T150000Z DTSTAMP:20260423T005757Z UID:AGNTISTA/24 DESCRIPTION:Title: An arithmetic count of rational plane curves\nby Kirsten Wickelgren (Duke University\, North Carolina) as part of Algebraic Geometry and Numbe r Theory seminar - ISTA\n\n\nAbstract\nThere are finitely many degree d ra tional plane curves passing through 3d-1 points\, and over the complex num bers\, this number is independent of (generically) chosen points. For exam ple\, there are 12 degree 3 rational curves through 8 points\, one conic p assing 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\, follow ing 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\, strengthe ning a count of Marc Levine. This is joint work with Jesse Kass\, Marc Lev ine\, and Jake Solomon.\n LOCATION:https://researchseminars.org/talk/AGNTISTA/24/ END:VEVENT END:VCALENDAR