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SUMMARY:María Angélica Cueto (Ohio State University)
DTSTART:20200506T200000Z
DTEND:20200506T210000Z
DTSTAMP:20260423T040115Z
UID:AG-Davis/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/3/"
 >Combinatorics and real lifts of bitangents to tropical quartic curves</a>
 \nby María Angélica Cueto (Ohio State University) as part of UC Davis al
 gebraic geometry seminar\n\n\nAbstract\nSmooth algebraic plane quartics ov
 er algebraically closed fields have 28 bitangent lines. By contrast\, thei
 r tropical counterparts have infinitely many bitangents. They are grouped 
 into seven equivalence classes\, one for each linear system associated to 
 an effective tropical theta characteristic on the tropical quartic curve.\
 n\nIn this talk\, I will discuss recent work joint with Hannah Markwig (ar
 xiv:2004.10891) on the combinatorics of these bitangent classes and its co
 nnection to the number of real bitangents to real smooth quartic curves ch
 aracterized by Pluecker. We will see that they are tropically convex sets 
 and they come in 39 symmetry classes. The classical bitangents map to spec
 ific vertices of these polyhedral complexes\, and each tropical bitangent 
 class captures four of the 28 bitangents. We will discuss the situation ov
 er the reals and show that each tropical bitangent class has either zero o
 r four lifts to classical bitangent defined over the reals\, in agreement 
 with Pluecker's classification.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/3/
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