相关论文: Model Theory of Compact Complex Manifolds with an …

Motivated by the study of meromorphic vector fields, a model theory of "compact complex manifolds equipped with a generic derivation" is here proposed. This is made precise by the notion of a differential CCM-structure. A first-order…

The theory of difference-differential fields of characteristic zero has a model-companion denoted by $\it DCFA$. Previously we proved a weak version of Zilber's dichotomy for $\it DCFA$. In this paper we use arc spaces techniques as…

We prove that the theory of differentially closed fields of characteristic zero in $m\geq 1$ commuting derivations DCF$_{0,m}$ satisfies the expected form of the dichotomy. Namely, any minimal type is either locally modular or nonorthogonal…

We prove that the group of Hamiltonian automorphisms of a symplectic 4-manifold contains only finitely many conjugacy classes of maximal compact tori with respect to the action of the full symplectomorphism group. We also extend to rational…

We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and prove that it satisfies the Zilber dichotomy…

In this paper we study M-theory compactifications on seven-dimensional manifolds with SU(3) structure. As such manifolds naturally pick out a specific direction, the resulting effective theory can be cast into a form which is similar to…

We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $\Gamma$ is a cocompact lattice in $\mathrm{Sl}(n, \mathbb R)$, $M$ is a compact manifold, and…

This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is…

Geometric sigma models are purely geometric theories of scalar fields coupled to gravity. Geometrically, these scalars represent the very coordinates of space-time, and, as such, can be gauged away. A particular theory is built over a given…

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater…

In this paper, we first construct $k$-dimensional compact complex manifolds from automorphisms of $\mathbb{C}^k$ which admit a fixed attracting point at infinity. Then, we charactize the fundamental group as well as the universal covering…

We study the automorphisms of compact K\"ahler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that…

In [1] it was shown that K^, a certain differential cohomology functor associated to complex K-theory, satisfies the Mayer-Vietoris property when the underlying manifold is compact. It turns out that this result is quite general. The work…

Given a compact, connected Lie group $K$, we use principal $K$-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let $M$ be a compact, connected, smooth manifold which supports an almost free…

We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold $X$ to an…

In [1] it was shown that K^, a certain differential cohomology functor associated to complex K-theory, satisfies the Mayer-Vietoris property when the underlying manifold is compact. It turns out that this result is quite general. The work…

We study new compactifications of the SO(32) heterotic string theory on compact complex non-Kahler manifolds. These manifolds have many interesting features like fewer moduli, torsional constraints, vanishing Euler character and vanishing…

In this paper we show that embedded and compact $C^1$ manifolds have finite integral Menger curvature if and only if they are locally graphs of certain Sobolev-Slobodeckij spaces. Furthermore, we prove that for some intermediate energies of…

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant…

Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem…