Pure Math · Mathematics & Statistics
Algebraic Geometry
The newest papers in Algebraic Geometry that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
27 papers, from 15 September 2026 to 5 November 2026: 27 arXiv preprints.
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Newest papers
Uniform Three-Fold Product Expansion of Algebraic-Geometry Codes over a Fixed Field
A collection of classical codes $C_1,\dots,C_m$ has product expansion if every low-weight word in the sum of their extensions to the product space can be written as a sum of words supported on few…Common zeros of homogeneous polynomials and the weight hierarchy of projective Reed-Muller codes
We determine the maximum number of common zeros in projective space of any set of linearly independent homogeneous polynomials of the same degree, when the degree is smaller than the cardinality of…Geometric Obstructions and Sharp Genus Dependence in LCD Scalings
We study the least pole order of a rational function whose nonzero evaluations scale a prescribed code to a Euclidean LCD code.Substantially Improved Rate and Distance for Addressable Transversal Phase Gates
An important ingredient in fault-tolerant quantum computation is asymptotically good codes with fully addressable transversal non-Clifford gates.Quantum error correcting codes from quiver moduli: Grassmannians, cyclic monodromy, and argyle collision divisors
Building on aspects of a recent diagrammatic field-theory programme for quantum error correction put forward by the first-named author (arXiv:2607.08911), we construct exact finite-dimensional codes…MDS Algebraic Geometry Codes of Square-Root Length on Hyperelliptic Curves
For every fixed genus $g\geq2$ and every $0<ρ<1$, we construct maximum distance separable (MDS) algebraic geometry codes over $\F_q$ for all sufficiently large odd squares $q$.Polynomial Residual Networks are Generically Identifiable
We prove identifiability results for constant-width residual networks with polynomial activations and bias terms.Structure and Exact Certification of Nonnegative Tensor Decompositions
We study the structure and exact certification of nonnegative tensor decompositions supplied through rational factor matrices.On the gradient conjecture at infinity: Finite spherical length for gradient trajectories of definable potentials
We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $θ(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has…Geometric knowledge spaces, Attention pairing and Architectures
In this paper, we propose a geometric approach to deriving attention mechanisms and exploring potential new transformer architectures.Do Neural Models Prefer Their Submodels?
A neural model is the set of functions that can be expressed by a given neural network architecture.Generic finiteness of solutions to parametrized systems of generalized polynomial inequalities
We study parametrized systems of $\mathit{generalized}$ polynomial inequalities, $(c \circ x^B) \in C$, for a positive variable vector $x \in \mathbb{R}^n_>$, a $\mathit{real}$ exponent matrix $B…Semi-supervised learning on singular data sets
We propose to model singular data clouds by subanalytic sets, and develop an approach to semi-supervised learning in this setting.Upper bounds on the number of images produced by point-mass lenses at different distances
If a light source is sequentially lensed by $n$ intervening point-mass lenses at distinct distances, the number of isolated images for a generic source position cannot be greater than $2\cdot…Deep Learning of Topological Equivalence Classes
We demonstrate an application of deep learning to the problem of identifying whether two generating vectors correspond to topologically equivalent finite group actions on Riemann surfaces, showing…Linear Independence of Polynomial Compositions with Bounded Input Degree
We prove the weak composition-independence conjectures of Kohn, Marchetti, Massarenti and Mella.Testing Algebraic Complete Intersections
Given independent and identically distributed samples samples from a probability distribution in a potentially high-dimensional real space, we study the problem of testing whether the distribution…Quantum geometry at arbitrary genus - I: Anharmonic potentials
In quantum mechanics of genus-1 potentials, perturbation theory around the topologically trivial saddle and non-perturbative instanton saddle are constructively related via the P/NP relation.Decoy and disclosure radii of invariant shape descriptors
A recognizer that compares rotation-invariant descriptors sees a surface only up to the fiber of the descriptor.Explicit tensors beyond the linear flattening barrier
We construct explicit n x n x n tensors of border rank at least 3n-o(n), improving the previous record of (2 + $\varepsilon$)n due to (Landsberg and Michalek 2025).