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Torsion of elliptic curves and unlikely intersections
P. 19-38.
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
Keywords: elliptic curve
Publication based on the results of:
In book
Oxford : Oxford University Press, 2018
Ornea L., Verbitsky M., Mathematische Zeitschrift 2021 Vol. 299 P. 2287-2296
A compact complex manifold V is called Vaisman if it admits an Hermitian metric which is conformal to a K\"ahler one, and a non-isometric conformal action by C. It is called quasi-regular if the C-action has closed orbits. In this case the corresponding leaf space is a projective orbifold, called the quasi-regular quotient of V. It is known that the set ...
Added: November 14, 2021
Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384-393
We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...
Added: October 26, 2016
Malygina E., Кунинец А. А., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83-105
We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes constituting error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove ...
Added: March 19, 2024
Matveeva A., Poberezhny V. A., Mathematical notes 2017 Vol. 101 No. 1 P. 115-122
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...
Added: May 22, 2017
Pavlov A., / Cornell University. Series arXiv "math". 2017. No. 1711.08130.
Let E be a smooth elliptic curve over ℂ. For E embedded into ℙ2 as Hesse cubic and V an Ulrich bundle on E we derive an explicit presentation of V using Moore matrices and theta functions. ...
Added: October 9, 2018
A. O. Radomskii, Izvestiya: Mathematics 2023 Vol. 87 No. 1 P. 113-153
We obtain some results related to Romanoff’s theorem. ...
Added: September 8, 2023
Serge Lvovski, Springer, 2020
This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they ...
Added: October 27, 2020
Шагай М. А., Флегонтов А. В., Иофе М. Д., Springer 2021
In our paper we seek to find of constructive describe functional classes defined on subsets of the period's parallelogram of doubly periodic Weierstrass functions using the integral norm. ...
Added: February 6, 2023
Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597-613
We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...
Added: August 30, 2019
Pavlov A., Buchweitz R., L’ENSEIGNEMENT MATHÉMATIQUE 2021
We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves. ...
Added: November 13, 2021
Buryak A., Moscow Mathematical Journal 2023 Vol. 23 No. 3 P. 309-317
An algorithm to determine all the Gromov–Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov–Witten invariants in terms of the stationary ones. In the case of an ...
Added: November 20, 2023
Matveeva A., Poberezhny V. A., Математические заметки 2017 Т. 101 № 1 С. 91-100
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and an explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...
Added: October 18, 2016
Pavlov A., Journal of Algebra 2019 Vol. 526 P. 211-242
We apply Orlov's equivalence to derive formulas for the Betti numbers of maximal Cohen-Macaulay modules over the cone an elliptic curve $(E,x)$ embedded into $\mathbb{P}^{n-1}$, by the full linear system $|\mathcal{O}(nx)|$, for $n>3$. The answers are given in terms of recursive sequences. These results are applied to give a criterion of (Co-)Koszulity.
In the last two ...
Added: May 24, 2019
Netay I. V., Savvateev A. V., Bulletin of the Korean Mathematical Society 2017 Vol. 54 No. 5 P. 1597-1617
The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely ...
Added: April 11, 2018