BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alheydis Geiger (Universität Tübingen) DTSTART:20210122T130000Z DTEND:20210122T140000Z DTSTAMP:20260422T172402Z UID:TGiZ/13 DESCRIPTION:Title: De formations of bitangent classes of tropical quartic curves\nby Alheydi s Geiger (Universität Tübingen) as part of Tropical Geometry in Frankfur t/Zoom TGiF/Z\n\n\nAbstract\nOver an algebraically closed field a smooth q uartic curve has 28 bitangent lines. Plücker proved that over the real nu mbers we have either 4\, 8\, 16 or 28 real bitangents to a real quartic cu rve. A tropical smooth quartic curve has exactly 7 bitangent classes which each lift either 0 or 4 times over the real numbers. The shapes of these bitangent classes have been classified by Markwig and Cueto in 2020\, who also determined their real lifting conditions.\nHowever\, for a fixed unim odular triangulation different choices of coefficients imply different edg e lengths of the quartic and these can change the shape of the 7 bitangent classes and might therefore influence their real lifting conditions.\nIn order to prove Plückers Theorem about the number of real bitangents tropi cally\, we have to study these deformations of the bitangent shapes. In a joint work with Marta Panizzut we develope a polymake extension\, which co mputes the tropical bitangents. For this we determine two refinements of t he secondary fan: one for which the bitangent shapes in each cone stay con stant and one for which the lifting conditions in each cone stay constant. \nThis is still work in progress\, but there will be a small software demo nstration.\n LOCATION:https://researchseminars.org/talk/TGiZ/13/ END:VEVENT END:VCALENDAR