Related papers: Characteristic forms of complex Cartan geometries

We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…

We treat two quite different problems related to changes of complex structures on K\"ahler manifolds by using global geometric method. First, by using operators from Hodge theory on compact K\"ahler manifold, we present a closed explicit…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

We study $p$-torsion Brauer classes in positive characteristic arising from differential forms. We relate this construction to the Brauer group of supersingular K3 surfaces and analyze the contribution of these classes to the Brauer-Manin…

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism…

Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.

We introduce a method to estimate the size of the domain of definition of the solutions of a meromorphic vector field on a neighborhood of its pole divisor. The corresponding techniques are, in a certain sense, quantitative versions of some…

This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

We construct a (non K\"ahler) compact complex 3-dimensional manifold $X$ having two following properties: 1) for any domain $D$ in $C^2$ every meromorphic map $f$ from this domain into $X$ extends to a meromorphic map from the envelope of…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…

In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…

We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…

Let k be a field and n > 0. There exists a DG k-module (V,d) and various approximations d + t d_1 + t^2 d_2 + ... + t^n d_n to a differential on V[[t]], one of which is a non-trivial deformation, another is obstructed, and another is…

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson…

Axiomatizing covarieties of coalgebras for an endofunctor is less intuitive than axiomatizing varieties of algebras via equations (Dahlqvist and Schmid, 2022). Existing techniques come from coalgebraic modal logic, pattern avoidance…

We compute explicit transgression forms for the Euler and Pontrjagin classes of a Riemannian manifold $M$ of dimension 4 under a conformal change of the metric, or a change to a Riemannian connection with torsion. These formulae describe…

The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum…