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We survey new results on finite groups of birational transformations of algebraic varieties.

Algebraic Geometry · Mathematics 2021-12-28 Yuri Prokhorov

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…

Algebraic Geometry · Mathematics 2010-03-31 Tristram de Piro

In this paper, we present a detailed mathematical description of the error correction process for Kitaev's model for finite Abelian groups. The number of errors Kitaev's model can correct depends on the lattice and its topology. Although…

Quantum Algebra · Mathematics 2024-04-15 Shawn X. Cui , César Galindo , Diego Romero

We correct an error in a technical lemma of Drees and Rootz\'en (2010) [arXiv:0910.0343] and discuss consequences for applications.

Statistics Theory · Mathematics 2015-11-02 Holger Drees , Holger Rootzén

Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…

This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability and the other on Sheaf Models in Algebraic Set Theory.

Logic · Mathematics 2007-10-17 Benno van den Berg , Ieke Moerdijk

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

Algebraic Topology · Mathematics 2019-09-11 Ramandeep Singh Arora

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…

Numerical Analysis · Mathematics 2026-02-04 Lutz Angermann

We propose an algebraic setup for end-to-end physical-layer network coding based on submodule transmission. We introduce a distance function between modules, describe how it relates to information loss and errors, and show how to compute…

Information Theory · Computer Science 2016-11-15 Elisa Gorla , Alberto Ravagnani

In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to…

Mathematical Physics · Physics 2024-02-28 Giorgio Gubbiotti

In this paper, we give a approximation characterization, embedding properties and the duality of matrix weighted modulation spaces.

Functional Analysis · Mathematics 2024-08-29 Shengrong Wang , Pengfei Guo , Jingshi Xu

In this revised version, we add some expository material and references and make some minor corrections.

alg-geom · Mathematics 2008-02-03 Robert Friedman , John W. Morgan

The theory of p-local compact groups, developed in an earlier paper by the same authors, is designed to give a unified framework in which to study the p-local homotopy theory of classifying spaces of compact Lie groups and p-compact groups,…

Algebraic Topology · Mathematics 2014-11-26 Carles Broto , Ran Levi , Bob Oliver

The contents of this paper has been incorporated into math.CO/0308288.

Combinatorics · Mathematics 2007-05-23 L. M. Pretorius , K. J. Swanepoel

We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its…

Number Theory · Mathematics 2016-04-06 Norifumi Ojiro

The article gives explicit calculation and interpretation of the additional locally anisotropic effects. Double role of the resulted gauge like fields discussed.

High Energy Physics - Theory · Physics 2007-05-23 Sergiu Ostaf

In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…

We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…

Commutative Algebra · Mathematics 2020-11-17 Omar Leon Sanchez , Alexey Ovchinnikov

The article surveys published and not yet published results about moduli spaces of algebraic surfaces.

Algebraic Geometry · Mathematics 2008-12-24 Fabrizio Catanese

This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…

Complex Variables · Mathematics 2009-09-25 J. Noguchi , T. Ochiai