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pro vyhledávání: '"Brugallé, Erwan"'
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 type of the curve. From this follows that a generic real algebr
Externí odkaz:
http://arxiv.org/abs/2402.03993
We show that, once translated to the dual setting of convex triangulations of lattice polytopes, results and methods from previous tropical works by Arnal-Renaudineau-Shaw, Renaudineau-Shaw, Renaudineau-Rau-Shaw, and Jell-Rau-Shaw extend to non-conve
Externí odkaz:
http://arxiv.org/abs/2209.14043
Autor:
Brugallé, Erwan, Schaffhauser, Florent
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 6 (January 6, 2023) epiga:8793
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 the base curve itself is maximal. This provides a new family of maximal
Externí odkaz:
http://arxiv.org/abs/2111.10959
Autor:
Brugallé, Erwan
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 part. This has originally been proved by Itenberg in the case of surfac
Externí odkaz:
http://arxiv.org/abs/2110.09173
Tropical refined invariants of toric surfaces constitute a fascinating interpolation between real and complex enumerative geometries via tropical geometry. They were originally introduced by Block and G\"ottsche, and further extended by G\"ottsche an
Externí odkaz:
http://arxiv.org/abs/2011.12668
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Autor:
Brugallé, Erwan
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 seem to have been made before. Our main result is that when $X$ is a re
Externí odkaz:
http://arxiv.org/abs/1811.06891
Publikováno v:
European Journal of Mathematics, 5 (2019), no. 3, 686--711
We address the problem of the maximal finite number of real points of a real algebraic curve (of a given degree and, sometimes, genus) in the projective plane. We improve the known upper and lower bounds and construct close to optimal curves of small
Externí odkaz:
http://arxiv.org/abs/1807.03992
We study the maximal values of Betti numbers of tropical subvarieties of a given dimension and degree in $\mathbb{TP}^n$. We provide a lower estimate for the maximal value of the top Betti number, which naturally depends on the dimension and degree,
Externí odkaz:
http://arxiv.org/abs/1707.09381
Publikováno v:
Ãpijournal de Géométrie Algébrique, Volume 1 (September 1, 2017) epiga:2030
Haas' theorem describes all partchworkings of a given non-singular plane tropical curve $C$ giving rise to a maximal real algebraic curve. The space of such patchworkings is naturally a linear subspace $W_C$ of the $\mathbb{Z}/2\mathbb{Z}$-vector spa
Externí odkaz:
http://arxiv.org/abs/1609.01979