Related papers: Weak equivalence classes of complex vector bundles

We study the $(k,s)$-positivity for holomorphic vector bundles on compact complex manifolds. $(0,s)$-positivity is exactly the Demailly $s$-positivity and a $(k,1)$-positive line bundle is just a $k$-positive line bundle in the sense of…

Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v. If v is primitive, than it is expected that M(v) is deformation equivalent to some Hilbert scheme and weight two hogde structure can be described by H^*(X,Z).…

We give necessary and sufficient conditions to specify vector bundles of conformal blocks for $\mathfrak{sl}_{2m}$ with rectangular weights which have ranks zero, one, and larger than one. First Chern classes of rank one bundles are shown…

Let $m\geq 2$ be a positive integer. Given a set $E(\omega )\subseteq \mathbb{N}$ we define $r_{N}^{(m)}(\omega )$ to be the number of ways to represent $N\in \mathbb{Z}$ as any combination of sums $\textit{ and }$ differences of $m$…

We construct Chern-Weil classes on infinite dimensional vector bundles with structure group contained in the algebra $\cl[\leq 0](M, E)$ of non-positive order classical pseudo-differential operators acting on a finite rank vector bundle $E$…

We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Afterwards we use the bounded rational sections of a…

For elliptic principal bundles $\pi:X\ra B$ over K\"ahler manifolds it was shown by Blanchard that $X$ has a K\"ahler metric if and only both Chern classes (with real coefficients) of $\pi$ vanish. For some elliptic principal bundles, when…

This paper deals with the question of J.Morava on existence of canonical complex cobordism class of singular submanifold. We present several solutions of this question for $X_r(\xi)$ -- the set of points where $\dim\xi-r+1$ generic sections…

Let h be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU is equipped with a structure of conjugation…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

In this paper, we prove the positivity of the double mixed discriminant associated with a positive linear map between spaces of third-order complex matrices, thereby settling the three-dimensional case of Finski's open problem. As an…

On a smooth complex projective variety $X$ of dimension $n$, consider an ample vector bundle $\mathcal{E}$ of rank $r \leq n-2$ and an ample line bundle $H$. A numerical character $m_2=m_2(X,\mathcal{E},H)$ of the triplet…

We study the existence of almost complex structures on even-dimensional sphere bundles over complex projective spaces. For bundles $\xi_{n,q}$ with fibre $S^{2q}$ over $\mathbb{C} P^n$, we establish a necessary condition: if $q \ge a(n)$…

Let $X$ be a $d$ dimensional projective manifold, $E$ be an ample vector bundle on $X$ and $0\le \lambda_N\le \lambda_{N-1} \le \cdots \le \lambda_1 \le \operatorname{rank}(E)$ be a partition of $d-2$. We prove that the Schur class…

We construct pairs of compact K\"ahler-Einstein manifolds $(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class $[\omega_i/2\pi]$, and for…

We classify nef vector bundles on a smooth quadric surface with first Chern class $(2,2)$ over an algebraically closed field of characteristic zero.

The tangent bundle $T^kM$ of order $k$, of a smooth Banach manifold $M$ consists of all equivalent classes of curves that agree up to their accelerations of order $k$. In the previous work of the author he proved that $T^kM$, $1\leq k\leq…

We show the existence of uniformly bounded sequences of increasing numbers of orthonormal sections of powers $L^k$ of a positive holomorphic line bundle $L$ on a compact K\"ahler manifold $M$. In particular, we construct for each positive…

Here we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover we show that every rank $r>2$ weakly uniform vector bundle with splitting type $a_{1,1}=...=a_{r,s}=0$ is trivial and every rank $r>2$ uniform…

Let M be a smooth manifold, and let O(M) be the poset of open subsets of M. Let C be a category that has a zero object and all small limits. A homogeneous functor (in the sense of manifold calculus) of degree k from O(M) to C is called very…