Results 41 to 50 of about 230 (119)
Fortschritte der Physik, Volume 74, Issue 4, April 2026.ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré +4 more
wiley +1 more source
A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley +1 more source
Pseudo Kobayashi hyperbolicity of subvarieties of general type on abelian varieties [PDF]
Journal of the Mathematical Society of Japan, 2019 We prove that the Kobayashi pseudo distance of a closed subvariety $X$ of an abelian variety $A$ is a true distance outside the special set $\operatorname{Sp}(X)$ of $X$, where $\operatorname{Sp}(X)$ is the union of all positive dimensional translated abelian subvarieties of $A$ which are contained in $X$.
openaire +2 more sources
Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms
Mathematika, Volume 72, Issue 2, April 2026.Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
wiley +1 more source
Regularity on abelian varieties I
, 2003 We introduce the notion of Mukai regularity ($M$-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and strengthens ...
Pareschi G., Popa M.
core +1 more source
Graph potentials and topological quantum field theories
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans +2 more
wiley +1 more source
Totally geodesic subvarieties in the moduli space of curves
, 2020 In this paper, we study totally geodesic subvarieties Y Ag of the moduli space of principally polarized abelian varieties with respect to the Siegel metric, for g ≥ 4. We prove that if Y is generically contained in the Torelli locus, then dim Y ≤ (7g - 2)
Pirola, Gian Pietro +2 more
core +1 more source
Equivariant toric geometry and Euler–Maclaurin formulae
Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 451-557, March 2026.Abstract We first investigate torus‐equivariant motivic characteristic classes of toric varieties, and then apply them via the equivariant Riemann–Roch formalism to prove very general Euler–Maclaurin‐type formulae for full‐dimensional simple lattice polytopes.
Sylvain E. Cappell +3 more
wiley +1 more source
Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
The motive of the Hilbert scheme of points in all dimensions
Proceedings of the London Mathematical Society, Volume 132, Issue 3, March 2026.Abstract We prove a closed formula for the generating series Zd(t)$\mathsf {Z}_d(t)$ of the motives [Hilbd(An)0]$[\operatorname{Hilb}^d({\mathbb {A}}^n)_0]$ in K0(VarC)$K_0(\operatorname{Var}_{{\mathbb {C}}})$ of punctual Hilbert schemes, summing over n$n$, for fixed d>0$d>0$.
Michele Graffeo +3 more
wiley +1 more source