Results 51 to 60 of about 3,053 (239)

Connections on trivial vector bundles over projective schemes

Comptes Rendus. Mathématique
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation.
Biswas, Indranil, Hô Hai, Phùng, dos Santos, Joao Pedro   +2 more
doaj   +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, Shin‐ichi Matsumura, Niklas Müller   +2 more
wiley   +1 more source

Dimensions of Prym varieties

International Journal of Mathematics and Mathematical Sciences, 2001
Given a tame Galois branched cover of curves π:X→Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula
Amy E. Ksir
doaj   +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

COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES

Forum of Mathematics, Sigma, 2016
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj   +1 more source

The Determination of Galois Groups [PDF]

Mathematics of Computation, 1973
A technique is described for the nontentative computer determination of the Galois groups of irreducible polynomials with integer coefficients. The technique for a given polynomial involves finding high-precision approximations to the roots of the polynomial, and fixing an ordering for these roots.
openaire   +2 more sources

Periodic points of rational functions over finite fields

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract For q$q$ a prime power and ϕ$\phi$ a rational function with coefficients in Fq$\mathbb {F}_q$, let p(q,ϕ)$p(q,\phi)$ be the proportion of P1Fq$\mathbb {P}^1\left(\mathbb {F}_q\right)$ that is periodic with respect to ϕ$\phi$. Furthermore, if d$d$ is a positive integer, let Qd$Q_d$ be the set of prime powers coprime to d!$d!$ and let P(d,q ...
Derek Garton
wiley   +1 more source

Explicit height estimates for CM curves of genus 2

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey, Samuel Le Fourn, Elisa Lorenzo García   +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

Diophantine Equation Generated by the Subfield of a Circular Field

Учёные записки Казанского университета: Серия Физико-математические науки
Two forms f (x, y, z) and g(x, y, z) of degree 3 were constructed, with their values being the norms of numbers in the subfields of degree 3 of the circular fields K13 and K19 , respectively.
I. G. Galyautdinov, E. E. Lavrentyeva
doaj   +1 more source