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DTSTART:20210328T030000
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DTSTAMP:20210514T124109Z
UID:1610632800@ist.ac.at
DTSTART:20210114T150000
DTEND:20210114T160000
DESCRIPTION:Speaker: Kirsten Wickelgren\nhosted by Timothy Browning\nAbstra
ct: There are finitely many degree d rational plane curves passing through
3d-1 points\, and over the complex numbers\, this number is independent o
f (generically) chosen points. For example\, there are 12 degree 3 rationa
l curves through 8 points\, one conic passing through 5\, and one line pas
sing through 2. Over the real numbers\, one can obtain a fixed number by w
eighting 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 t
he presence of a common generalization\, valid over a general field. We de
velop and compute an A1-degree\, following Morel\, of the evaluation map o
n 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 point
s with fixed residue fields\, strengthening a count of Marc Levine. This i
s joint work with Jesse Kass\, Marc Levine\, and Jake Solomon.
LOCATION:https://mathseminars.org/seminar/AGNTISTA\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:An arithmetic count of rational plane curves
URL:https://talks-calendar.app.ist.ac.at/events/2882
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