53 citations · 136 across the 20 of their papers we have counts for
14 papers · 1 filter
Maximality of moduli spaces of vector bundles on curves
Erwan Brugallé, Florent Schaffhauser
We prove that moduli spaces of semistable vector bundles of coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if th…
Euler characteristic and signature of real semi-stable degenerations
Erwan Brugallé
We give a motivic proof of the fact that for non-singular real tropical complete intersections, the Euler characteristic of the real part is equal to the signature of the complex p…
On the invariance of Welschinger invariants
Erwan Brugallé
We collect in this note some observations about original Welschinger invariants of real symplectic fourfolds. None of their proofs is difficult, nevertheless these remarks do not s…
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…
Non-existence of torically maximal hypersurfaces
Erwan Brugallé, Grigory Mikhalkin, Jean-Jacques Risler +1
Torically maximal curves (known also as simple Harnack curves) are real algebraic curves in the projective plane such that their logarithmic Gauß map is totally real. In this paper…