Related papers: Almost Complex Structure on $S^{2n}$

In this paper, the singular-value decomposition theory of complex matrices is explored to study constantly curved 2-spheres minimal in both $\mathbb{C}P^n$ and the hyperquadric of $\mathbb{C}P^n$. The moduli space of all those noncongruent…

Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex…

We give a new proof of the classification due to Peternell-Szurek-Wi\'{s}niewski of nef vector bundles on a projective space with the first Chern class less than three and on a smooth hyperquadric with the first Chern class less than two…

Assuming Hartshorne's conjecture on complete intersections, we classify projective bundles over projective spaces which has a smooth blow up structure over another projective space. Under some assumptions, we also classify projective…

We study embeddings of the unit sphere of complex Hilbert spaces of dimension a power $2^n$ into the corresponding groups of non-singular linear transformations. For the case of $n=1$, the sphere $S_2$ of qubits is identified with…

Comparing to the Chen-Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods…

One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…

We investigate relative connections on a sheaf of modules. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic vector bundle over a complex analytic family. We show that the relative Chern…

The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…

In this article, we prove that there does not exist a family of entire curves in the universal family of hypersurfaces of degree $d\geq 2n$ in the complex projective space ${\mathbb P}^n$. This can be seen as a weak version of the Kobayashi…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

We prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, we prove that all flexible fillings are symplectomorphic. As an application,…

An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $\psi$.…

Let $M_c=M(2,0,c)$ be the moduli space of O(1)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0$ and $c_2=c$ on a K3 surface $X$ where O(1) is a generic ample line bundle on $X$. When $c=2n\geq4$ is even, $M_c$ is a singular…

In this article we study the Gieseker-Maruyama moduli spaces $\mathcal{B}(e,n)$ of stable rank 2 algebraic vector bundles with Chern classes $c_1=e\in\{-1,0\},\ c_2=n\ge1$ on the projective space $\mathbb{P}^3$. We construct two new…

In this semi-expository note, we give a new proof of a structure theorem due to Shimura for nearly holomorphic modular forms on the complex upper half plane. Roughly speaking, the theorem says that the space of all nearly holomorphic…

We study the topology of Vietoris--Rips complexes of finite grids on the torus. Let $T_{n,n}$ be the grid of $n\times n$ points on the flat torus $S^1\times S^1$, equipped with the $l^1$ metric. Let $\mathrm{VR}(T_{n,n};k)$ be the…

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…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

We study constraints on the Chern classes of a vector bundle on a singular variety. We use this constraint to study a variety which carries a Hodge cycle that are not a linear combination of Chern classes of vector bundles on it.