Related papers: Linear foliations of complex spheres I. Chains

These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…

We show analogues of the classical Krein-Milman theorem for several ordered algebraic structures, especially in a semilattice (non-linear) framework. In that case, subsemilattices are seen as convex subsets, and for our proofs we use…

We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field…

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard…

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the…

We consider an extended version of the Kerr theorem incorporated in the Kerr-Schild formalism. It allows one to construct the series of exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of…

A famous conjecture attributed to Kodaira asks whether any compact Kaehler manifold can be approximated by projective manifolds. We confirm this conjecture on projectivized direct sums of three line bundles on three-dimensional complex tori…

This is the first of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher version of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based on…

We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott. Then we consider the direct image of a…

Following T. Suwa, we study unfoldings of algebraic foliations and their relationship with families of foliations, making focus on those unfoldings related to trivial families. The results obtained in the study of unfoldings are then…

We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit,…

We study certain foliated complex manifolds that behave similarly to complete nonsingular toric varieties. We classify them by combinatorial objects that we call marked fans. We describe the basic cohomology algebras of them in terms of…

The Worldline Quantum Field Theory (WQFT) has proven to be an efficient tool for calculating observables in gravitational wave physics. In contrast to other QFT-based techniques in the realm of gravitational wave physics, it makes the…

The monodromy of almost toric Lagrangian fibrations on the complex projective plane is described.

We enumerate smooth rational curves on very general Weierstrass fibrations over hypersurfaces in projective space. The generating functions for these numbers lie in the ring of classical modular forms. The method of proof uses topological…

Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart-free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation…

We construct the effective theory of electrically charged, spatially extended, infinitely heavy objects at leading power. The theory may be viewed as a generalization of NRQED for particles with a finite charge distribution where the charge…

We prove multiple generalizations of Fan's combinatorial labeling result for sphere triangulations. This can be seen as a comprehensive extension of the Borsuk--Ulam theorem. In typical applications, the Borsuk--Ulam theorem gives…

Attempts to build a discrete theory for rational maps on the sphere via circle packing have foundered on discretization effects in locating branch points. The authors remove this impediment by introducing generalized branch points. A…

We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…