Results 21 to 30 of about 12,524 (89)
Equivalent Birational Embeddings III: cones [PDF]
, 2013 Two divisors in $\mathbb P^n$ are said to be Cremona equivalent if there is a Cremona modification sending one to the other. In this paper I study irreducible cones in $\mathbb P^n$ and prove that two cones are Cremona equivalent if their general ...
Mella, Massimiliano
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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
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 +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 +2 more
wiley +1 more source
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
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
Arithmetic sparsity in mixed Hodge settings
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3511-3521, November 2025.Abstract Let X$X$ be a smooth irreducible quasi‐projective algebraic variety over a number field K$K$. Suppose X$X$ is equipped with a p$p$‐adic étale local system compatible with an admissible graded‐polarized variation of mixed Hodge structures on the complex analytification of XC$X_{\operatorname{\mathbb {C}}}$.
Kenneth Chung Tak Chiu
wiley +1 more source
Continua of periodic points for planar integrable rational maps [PDF]
, 2016 We present three alternative methodologies to find continua of periodic points with a prescribed period for rational maps having rational first integrals.
Gasull Embid, Armengol +2 more
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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
wiley +1 more source
Special orbifolds and birational classification: a survey [PDF]
, 2010 We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this special case ...
Campana, Frederic
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