Bitangents to plane quartics via tropical geometry: rationality, -enumeration, and real signed count
We explore extensions of tropical methods to arithmetic enumerative problems such as A 1-
enumeration with values in the Grothendieck–Witt ring and rationality over Henselian valued …
enumeration with values in the Grothendieck–Witt ring and rationality over Henselian valued …
Combinatorics and real lifts of bitangents to tropical quartic curves
Smooth algebraic plane quartics over algebraically closed fields of characteristic different
than two have 28 bitangent lines. Their tropical counterparts often have infinitely many …
than two have 28 bitangent lines. Their tropical counterparts often have infinitely many …
Avoidance loci and tropicalizations of real bitangents to plane quartics
We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one
coming from the closures of connected components of the avoidance locus and another …
coming from the closures of connected components of the avoidance locus and another …
Bitangents of real algebraic curves: signed count and constructions
T Blomme, E Brugallé, C Garay - arXiv preprint arXiv:2402.03993, 2024 - arxiv.org
We study real bitangents of real algebraic plane curves from two perspectives. We first show
that there exists a signed count of such bitangents that only depends on the real topological …
that there exists a signed count of such bitangents that only depends on the real topological …
Computing tropical bitangents to smooth quartic curves in polymake
A Geiger, M Panizzut - Journal of Symbolic Computation, 2024 - Elsevier
In this article we introduce the recently developed polymake extension
TropicalQuarticCurves and its associated database entry in polyDB dealing with smooth …
TropicalQuarticCurves and its associated database entry in polyDB dealing with smooth …
Tropical geometric counting problems
ABM Geiger - 2022 - tobias-lib.ub.uni-tuebingen.de
A degeneration of algebraic counting problems to tropical geometry produces new concepts
and computational approaches. The challenge is to find methods to lift the results in the …
and computational approaches. The challenge is to find methods to lift the results in the …