Real inflection points of real linear series on real (hyper)elliptic curves (joint with I. Biswas and C. Garay López)

Algebra Seminar
Friday, September 14, 2018 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Ethan Cotterill – Universidade Federal Fluminense –
Yoav Len
According to Plucker's formula, the total inflection of a linear series (L,V) on a complex algebraic curve C is fixed by numerical data, namely the degree of L and the dimension of V. Equipping C and (L,V) with compatible real structures, it is more interesting to ask about the total real inflection of (L,V). The topology of the real inflectionary locus depends in a nontrivial way on the topology of the real locus of C. We study this dependency when C is hyperelliptic and (L,V) is a complete series. We first use a nonarchimedean degeneration to relate the (real) inflection of complete series to the (real) inflection of incomplete series on elliptic curves; we then analyze the real loci of Wronskians along an elliptic curve, and formulate some conjectural quantitative estimates.