Results 21 to 30 of about 47 (47)

Minimal projective varieties satisfying Miyaoka's equality

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract In this paper, we establish a structure theorem for a minimal projective klt variety X$X$ satisfying Miyaoka's equality 3c2(X)=c1(X)2$3c_2(X) = c_1(X)^2$. Specifically, we prove that the canonical divisor KX$K_X$ is semi‐ample and that the Kodaira dimension κ(KX)$\kappa (K_X)$ is equal to 0, 1, or 2. Furthermore, based on this abundance result,
Masataka Iwai, Shin‐ichi Matsumura, Niklas Müller   +2 more
wiley   +1 more source

Symmetric products and puncturing Campana‐special varieties

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett–Tschinkel using symmetric powers of uniruled surfaces, and propose a corrected conjecture inspired by Campana's conjectures on special varieties.
Finn Bartsch, Ariyan Javanpeykar, Aaron Levin   +2 more
wiley   +1 more source

Topological K‐theory of quasi‐BPS categories for Higgs bundles

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract In a previous paper, we introduced quasi‐BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi‐BPS categories (called BPS in this case) are noncommutative analogues of Hitchin integrable systems.
Tudor Pădurariu, Yukinobu Toda
wiley   +1 more source

Normal covering numbers for Sn$S_n$ and An$A_n$ and additive combinatorics

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3307-3325, November 2025.
Abstract The normal covering number γ(G)$\gamma (G)$ of a noncyclic group G$G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for γ(Sn)$\gamma (S_n)$ and γ(An)$\gamma (A_n)$ depending on the arithmetic structure of n$n$. In particular we determine the limsups over γ(Sn)/n$\gamma (S_n) / n$ and γ(An)
Sean Eberhard, Connor Mellon
wiley   +1 more source

The geometry and arithmetic of bielliptic Picard curves

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley   +1 more source

The relative Hodge–Tate spectral sequence for rigid analytic spaces

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract We construct a relative Hodge–Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of Qp$\mathbb {Q}_p$. To this end, we generalise Scholze's strategy in the absolute case by using smoothoid adic spaces.
Ben Heuer
wiley   +1 more source

On the finiteness of maps into simple abelian varieties satisfying certain tangency conditions

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2723-2730, September 2025.
Abstract We show that given a simple abelian variety A$A$ and a normal variety V$V$ defined over a finitely generated field K$K$ of characteristic zero, the set of non‐constant morphisms V→A$V \rightarrow A$ satisfying certain tangency conditions imposed by a Campana orbifold divisor Δ$\Delta$ on A$A$ is finite.
Finn Bartsch
wiley   +1 more source

Parity of ranks of Jacobians of curves

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser, Holly Green, Alexandros Konstantinou, Adam Morgan   +3 more
wiley   +1 more source

Moduli of finite flat torsors over nodal curves

Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.
Abstract We show that log flat torsors over a family X/S$X/S$ of nodal curves under a finite flat commutative group scheme G/S$G/S$ are classified by maps from the Cartier dual of G$G$ to the log Jacobian of X$X$. We deduce that fppf torsors on the smooth fiberss of X/S$X/S$ can be extended to global log flat torsors under some regularity hypotheses.
Sara Mehidi, Thibault Poiret
wiley   +1 more source

On torsion of abelian varieties over large algebraic extensions of finitely generated fields

Mathematika, 1984
Moshe Jarden
exaly