17 citations · 33 across the 11 of their papers we have counts for
12 papers
Planar Tropical Cubic Curves of Any Genus, and Higher Dimensional Generalisations
Benoît Bertrand, Erwan Brugallé, Lucía López de Medrano
We study the maximal values of Betti numbers of tropical subvarieties of a given dimension and degree in . We provide a lower estimate for the maximal value of the t…
Haas' theorem revisited
Benoît Bertrand, Erwan Brugallé, Arthur Renaudineau
Haas' theorem describes all partchworkings of a given non-singular plane tropical curve giving rise to a maximal real algebraic curve. The space of such patchworkings is natura…
On the total curvature of tropical hypersurfaces
Benoît Bertrand, Lucía López de Medrano, Jean-Jacques Risler
This paper studies the curvatures of amoebas and real amoebas (i.e. essentially logarithmic curvatures of the complex and real parts of a real algebraic hypersurface) and of tropic…
Genus 0 characteristic numbers of the tropical projective plane
Benoit Bertrand, Erwan Brugalle, Grigory Mikhalkin
Finding the so-called characteristic numbers of the complex projective plane is a classical problem of enumerative geometry posed by Zeuthen more than a century ag…
Tropical Open Hurwitz numbers
Benoit Bertrand, Erwan Brugalle, Grigory Mikhalkin
We give a tropical interpretation of Hurwitz numbers extending the one discovered in \cite{CJM}. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary…
On the number of connected components of the parabolic curve
Benoit Bertrand, Erwan Brugallé
We construct a polynomial of degree d in two variables whose Hessian curve has (d-2)^2 connected components using Viro patchworking. In particular, this implies the existence of a…