Related papers: Bimeromorphic geometry of K\"ahler threefolds

Motivated by the duality theory between Hermitian symmetric spaces of noncompact and compact types, we introduce and examine the concept of K\"ahler duality between domains of $\mathbb C^n$.

Let $M$ be a K\"ahler manifold with complex structure $J$ and K\"ahler metric $g$. A c-projective vector field is a vector field on $M$ whose flow sends $J$-planar curves to $J$-planar curves, where $J$-planar curves are analogs of what…

We prove that the abundance conjecture for non-uniruled klt pairs in dimension $n$ implies the abundance conjecture for uniruled klt pairs in dimension $n$, assuming the Minimal Model Program in lower dimensions.

Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial…

In an earlier work, we investigated some consequences of the existence of a K\"ahler metric of negative holomorphic sectional curvature on a projective manifold. In the present work, we extend our results to the case of semi-negative (i.e.,…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

We construct model hyper-K\"ahler geometries that include and generalize the multi-Ooguri-Vafa model using the formalism of Gaitto, Moore, and Neitzke. This is the first paper in a series of papers making rigorous Gaiotto--Moore--Neitzke's…

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized K\"ahler geometry. We investigate the reduction from (2,2) to…

We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is…

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\"ahler reduction; projective superspace; the generalized Legendre construction;…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a…

The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to K\"ahler geometry by several authors. In this paper we replace the strong notions of totally geodesic…

Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…

Rotation minimizing vector fields and frames were introduced by Bishop as an alternative to the Frenet frame. They are used in CAGD because they can be defined even the curvature vanishes. Nevertheless, many other geometric properties have…

This is a light and short review on the geometry of hypermultiplets coupled to supergravity and its appearance in string theory. As is long known, the target space of the hypermultiplet sigma-model is a quaternion-K\"ahler (QK) manifold of…

We study Lie algebras admitting para-K\"ahler and hyper-para-K\"ahler structures. We give new characterizations of these Lie algebras and we develop many methods to build large classes of examples. Bai considered para-K\"ahler Lie algebras…

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our…

We construct K\"ahler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each $r\geq 3$, we obtain large classes of K\"ahler groups that have classifying…

We evaluate the enumerative invariants of low degree on the mirror quintic threefold.

We prove that the Riemannian geometry of almost K\"ahler manifolds can be expressed in terms of the Poisson algebra of smooth functions on the manifold. Subsequently, K\"ahler-Poisson algebras are introduced, and it is shown that a…