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Let $\pi: X \to Y$ be a morphism of projective varieties and suppose that $\alpha$ is a pseudo-effective numerical cycle class satisfying $\pi_*\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha$ is a limit of…

Algebraic Geometry · Mathematics 2017-05-17 Mihai Fulger , Brian Lehmann

Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a…

Number Theory · Mathematics 2011-04-15 Benjamin Hutz

The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is…

Machine Learning · Computer Science 2022-09-23 Kathryn Heal , Avinash Kulkarni , Emre Can Sertöz

Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles…

Representation Theory · Mathematics 2025-03-13 Mikhail Borovoi , Willem A. de Graaf

We compute the equivariant homology and cohomology of projective spaces with integer coefficients. More precisely, in the case of cyclic groups, we show that the cellular filtration of the projective space $P(k\rho )$, of lines inside…

Algebraic Topology · Mathematics 2025-09-24 Samik Basu , Pinka Dey , Aparajita Karmakar

We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…

Algebraic Geometry · Mathematics 2015-12-16 Jaiung Jun

Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…

K-Theory and Homology · Mathematics 2013-11-21 David Wayne

Let $K$ be a field of characteristic $0$. We present an explicit algorithm that, given the invariants of a generic homogeneous polynomial $f$ under the linear action of $\mathrm{GL}_n$ or $\mathrm{SL}_n$, returns a polynomial differing from…

Commutative Algebra · Mathematics 2025-06-05 Thomas Bouchet

Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…

Rings and Algebras · Mathematics 2010-02-22 L. Delvaux , A. Van Daele

Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…

Algebraic Geometry · Mathematics 2012-06-12 Florian Block

We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…

Data Structures and Algorithms · Computer Science 2018-08-13 Michał Włodarczyk

We compute periods of perturbations of a Fermat variety. This allows us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions. We explore some examples and give an upper bound for the dimension of this…

Algebraic Geometry · Mathematics 2025-07-15 Jorge Duque Franco

We discuss recent developments in the study of semiorthogonal decompositions of algebraic varieties with an emphasis on their behaviour in families. First, we overview new results concerning homological projective duality. Then we introduce…

Algebraic Geometry · Mathematics 2021-11-02 Alexander Kuznetsov

We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…

High Energy Physics - Theory · Physics 2019-01-29 Fabian Fischbach , Albrecht Klemm , Christoph Nega

Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is,…

Optimization and Control · Mathematics 2011-01-31 Didier Henrion

We compute the number of $\mathcal{X}$-variables (also called coefficients) of a cluster algebra of finite type when the underlying semifield is the universal semifield. For classical types, these numbers arise from a bijection between…

Combinatorics · Mathematics 2019-02-26 Melissa Sherman-Bennett

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…

Machine Learning · Statistics 2018-05-15 Anthony Tompkins , Fabio Ramos

We study the algebraic hyperbolicity of certain subvarieties of homogeneous varieties, building on the techniques introduced by Coskun-Riedl, Yeong and Mioranci. This generalizes earlier known results for hypersurfaces to higher…

Algebraic Geometry · Mathematics 2025-11-10 Andy B. Day , Neelarnab Raha

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

Logic in Computer Science · Computer Science 2015-07-01 Guillaume Bonfante , Yves Guiraud

Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…

Discrete Mathematics · Computer Science 2024-01-17 Xiaoxiong Lu , Chengqing Li , Bo Zhou
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