Related papers: Complex line fields on almost-complex manifolds

In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results [J. Differential Geom., 21 (1985): 269-281] from Poincar\'e…

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax…

A countable CW complex $K$ is quasi-finite (as defined by A.Karasev) if for every finite subcomplex $M$ of $K$ there is a finite subcomplex $e(M)$ such that any map $f:A\to M$, where $A$ is closed in a separable metric space $X$ satisfying…

We provide a classification result on nearly free arrangements of lines in the complex projective plane with nodes and triple points.

We consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We obtain a description of their tangent bundles, compute their mod p…

The $\bar{\partial}_{_{J}}$ operator over an almost complex manifold induces canonical connections of type $(0,1)$ over the bundles of $(p,0)$-forms. If the almost complex structure is integrable then the previous connections induce the…

The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…

We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle of a singular…

Here we consider higher Chern classes of vector bundles of conformal blocks on $\overline{\operatorname{M}}_{0,n}$, giving explicit formulas for them, and extending various results that hold for first Chern classes to them. We use these…

We survey the history as well as recent progress in the Yang problem concerning the existence of complete bounded complex submanifolds of the complex Euclidean spaces. We also point out some open questions on the topic.

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

We show by example that the Chern numbers c_1^3 and c_1 c_2 of a complex 3-fold are not determined by the topology of the underlying smooth compact 6-manifold. In fact, we observe that infinitely many different values of a Chern number can…

For a compact smooth manifold with corners (or finite CW-complex) $X$, we can prescribe a finite set of spin or spin$^h$ manifolds (possibly with boundary) mapping into it so that every real vector bundle over $X$ is determined, up to…

From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In…

We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly…

We discuss notions of almost complex, complex and K\"{a}hler structures in the realm of non-commutative geometry and investigate them for a class of finite dimensional spectral triples on the three-point space. We classify all the almost…

F-manifolds are complex manifolds with a multiplication with unit on the holomorphic tangent bundle with a certain integrability condition. Here the local classification of 3-dimensional F-manifolds with or without Euler fields is pursued.

The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if $Z$ is a hypersurface in a compact complex manifold, defined…

We establish a necessary and sufficient condition for pairs of integers to arise as the weights at the fixed points of an effective circle action on a compact almost complex 4-manifold with a discrete fixed point set. As an application, we…