Related papers: Projective Isomonodromy and Galois Groups

A fundamental tool of Differential Galois Theory is the assignment of an algebraic group to each finite-dimensional differential module over differential field in such a way that the category of differential modules it generates is…

We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…

In the context of differential fields of characteristic zero with several commuting derivations, we discuss the notion of $\#$-differential equations on parameterized D-torsors and their associated Galois extensions. Using model-theoretic…

This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…

The isomonodromy deformation method is applied to the scaling limits in the linear NxN matrix equations with rational coefficients to obtain the deformation equations for the algebraic curves which describe the local behavior of the reduced…

The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.

The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of…

This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This…

The motivation for this paper is to extend the known model theoretic treatment of differential Galois theory to the case of linear difference equations (where the derivative is replaced by an automorphism.) The model theoretic difficulties…

We consider a linear meromorphic system in the Birkhoff standard form. The construction of the isomonodromic deformation of it proposed by Bolibruch is discussed. This construction has some special characteristics because of resonant…

We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending…

We carry out the generalized symmetry classification of polylinear autonomous discrete equations defined on the square, which belong to a twelve-parametric class. The direct result of this classification is a list of equations containing no…

A classical result of F.Klein states that, given a finite primitive group $G\subseteq SL_2(\mathbb{C})$, there exists a hypergeometric equation such that any second order LODE whose differential Galois group is isomorphic to $G$ is…

We characterize real elliptic differential systems whose solutions can be expressed in terms of holomorphic solutions to an associated holomorphic Pfaffian system $\mathcal H$ on a complex manifold. In particular, these elliptic systems…

We define a moduli space of stable regular singular parabolic connections of spectral type on smooth projective curves and show the smoothness of the moduli space and give a relative symplectic structure on the moduli space. Moreover, we…

We give a survey of Darboux type theorems in multisymplectic geometry. These theorems establish when a closed differential form of a certain type admits a constant-coefficient expression in some local coordinate system. Beyond the classical…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

For a differential field $F$ having an algebraically closed field of constants, we analyze the structure of Picard-Vessiot extensions of $F$ whose differential Galois groups are unipotent algebraic groups and apply these results to study…

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

In this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in…