25 citations · 66 across the 14 of their papers we have counts for
16 papers
Dolbeault Cohomology of Graphs and Berkovich Curves
Walter Gubler, Philipp Jell, Joseph Rabinoff
We introduce real-valued -forms on weighted metric graphs with boundary similar to Lagerberg forms on polyhedral spaces. We compute the Dolbeault cohomology and prove Poinca…
Forms on Berkovich spaces based on harmonic tropicalizations
Walter Gubler, Philipp Jell, Joseph Rabinoff
We introduce tropical skeletons for Berkovich spaces based on results of Ducros. Then we study harmonic functions on good strictly analytic spaces over a non-trivially valued non-A…
Pluripotential theory for tropical toric varieties and non-archimedean Monge-Ampére equations
José Ignacio Burgos Gil, Walter Gubler, Philipp Jell +1
Tropical toric varieties are partial compactifications of finite dimensional real vector spaces associated with rational polyhedral fans. We introduce plurisubharmonic functions an…
A comparison of positivity in complex and tropical toric geometry
J. I. Burgos Gil, W. Gubler, P. Jell +1
Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our ma…
Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
Philipp Jell, Hannah Markwig, Felipe Rincón +1
We study the moduli space of -dimensional linear subspaces contained in a fixed -dimensional linear variety , and its tropicalization. We prove that these moduli space…
Construction of Fully Faithful Tropicalizations for Curves in Ambient Dimension 3
Trevor Gunn, Philipp Jell
In tropical geometry, one studies algebraic curves using combinatorial techniques via the tropicalization procedure. The tropicalization depends on a map to an algebraic torus and…
Tropical cohomology with integral coefficients for analytic spaces
Philipp Jell
We study tropical Dolbeault cohomology for Berkovich analytic spaces, as defined by Chambert-Loir and Ducros. We provide a construction that lets us pull back classes in tropical c…
Real tropicalization and analytification of semialgebraic sets
Philipp Jell, Claus Scheiderer, Josephine Yu
Let be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that…
Constructing smooth and fully faithful tropicalizations for Mumford curves
Philipp Jell
The tropicalization of an algebraic variety X is a combinatorial shadow of X, which is sensitive to a closed embedding of X into a toric variety. Given a good embedding, the tropic…
Continuity of Plurisubharmonic Envelopes in Non-Archimedean Geometry and Test Ideals (with an Appendix by José Ignacio Burgos Gil and Martín Sombra)
Walter Gubler, Philipp Jell, Klaus Künnemann +1
Let L be an ample line bundle on a smooth projective variety X over a non-archimedean field K. For a continuous metric on L, we show in the following two cases that the semipositiv…
Lefschetz (1,1)-theorem in tropical geometry
Philipp Jell, Johannes Rau, Kristin Shaw
For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in…
Tropical Hodge numbers of non-archimedean curves
Philipp Jell
We study the tropical Dolbeault cohomology of non-archimedean curves as defined by Chambert-Loir and Ducros. We give a precise condition for when this cohomology satisfies Poincaré…
Poincaré duality for tropical Dolbeault cohomology of non-archimedean Mumford curves
Philipp Jell, Veronika Wanner
We calculate the tropical Dolbeault cohomology for the analytifications of the projective line and Mumford curves over non-archimedean fields. We show that the cohomology satisfies…
Differentiability of non-archimedean volumes and non-archimedean Monge-Ampère equations (with an appendix by Robert Lazarsfeld)
José Ignacio Burgos Gil, Walter Gubler, Philipp Jell +2
Let be a normal projective variety over a complete discretely valued field and a line bundle on . We denote by the analytification of in the sense of…
Superforms, Tropical Cohomology, and Poincaré Duality
Philipp Jell, Kristin Shaw, Jascha Smacka
We establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we pro…
A Poincaré lemma for real-valued differential forms on Berkovich spaces
Philipp Jell
Real-valued differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros in 'Formes différentielles réelles et courants sur les espaces de Berkovich'…