Results 21 to 30 of about 7,542 (104)
Local–global principles for semi‐integral points on Markoff orbifold pairs
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study local–global principles for semi‐integral points on orbifold pairs of Markoff type. In particular, we analyse when these orbifold pairs satisfy weak weak approximation, weak approximation and strong approximation off a finite set of places.
Vladimir Mitankin, Justin Uhlemann
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 +2 more
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Commensurating actions of birational groups and groups of pseudo-automorphisms [PDF]
Journal de l’École polytechnique — Mathématiques, 2019 Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on cat(0) cubical complexes, for example a discrete group with Kazhdan Property (T), is birationally conjugate to a ...
Cantat, Serge, de Cornulier, Yves
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Mirror symmetry, Laurent inversion, and the classification of Q$\mathbb {Q}$‐Fano threefolds
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We describe recent progress in a program to understand the classification of three‐dimensional Fano varieties with Q$\mathbb {Q}$‐factorial terminal singularities using mirror symmetry. As part of this we give an improved and more conceptual understanding of Laurent inversion, a technique that sometimes allows one to construct a Fano variety X$
Tom Coates +2 more
wiley +1 more source
Birational automorphisms of a three-dimensional double cone [PDF]
Sbornik: Mathematics, 1998 The author proves birational properties of a special three-dimensional algebraic variety \(X\) in \(\mathbb P^4 \). This variety is a double cover of a quadric cone \(Q\) in \(\mathbb P^4\), which is branched over a smooth section of \(Q\) with a quartic.
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, 2017 We determine positive-dimensional G-periodic proper subvarieties of an n-dimensional normal projective variety X under the action of an abelian group G of maximal rank n-1 and of positive entropy.
Hu, F., Tan, S., Zhang, D.
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On the section conjecture over fields of finite type
Mathematische Nachrichten, Volume 298, Issue 11, Page 3476-3493, November 2025.Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of Q$\mathbb {Q}$. This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus ≤2$\le 2$, and a basis of open subsets of any curve.
Giulio Bresciani
wiley +1 more source
Constraints on automorphism groups of higher dimensional manifolds
, 2013 In this note, we prove, for instance, that the automorphism group of a rational manifold X which is obtained from CP^k by a finite sequence of blow-ups along smooth centers of dimension at most r with k>2r+2 has finite image in GL(H^*(X,Z)).
Bayraktar, Turgay, Cantat, Serge
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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
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Cyclic cubic points on higher genus curves
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract The distribution of degree d$d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: d=3$d = 3$. For curves of genus at least 5, we show cubic points with Galois group C3$C_3$ arise from well‐structured morphisms, along with providing ...
James Rawson
wiley +1 more source