Related papers: Monads on multiprojective spaces and associated ve…

We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\to B as a Fourier transform of the S^1-equivariant J-function of the total space of V and show that it lies on the Givental…

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 prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of "goodness". In dimension one, for which goodness is…

Let M be a Poisson manifold and A a Weil algebra. We describe an isomorphism of cohomolgy algebra and proves that Poisson cohomology with values in A is isomorphic to the tensor product of A with Poisson cohomolgy with real values.

In this paper, we study holomorphic vector bundles on (diagonal) Hopf manifolds. In particular, we give a description of moduli spaces of stable bundles on generic (non-elliptic) Hopf surfaces. We also give a classification of stable rank-2…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

The moduli space M(r,d) of stable, rank r, degree d vector bundles on a smooth projective curve of genus g>1 is shown to be birational to M(h,0) x A, where h=hcf(r,d) and A is affine space of dimension (r^2-h^2)(g-1). The birational…

We are concerned with the problem of the stability of the syzygy bundles associated to base point free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from Mark Green's vanishing…

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…

The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is in general still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of…

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…

Given a quotient vector bundle $\mathcal A$ over $X$ with kernel map $\kappa: X\to\mathrm{Max}\,A$ we study the codual bundle with fiber at each point $x\in X$ isomorphic to the dual of $\kappa(x)$. Applying the adjunction between quotient…

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over…

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued…

Let X be a projective smooth holomorphic Poisson surface, in other words, whose anti-canonical divisor is effective. We show that moduli spaces of certain Bridgeland stable objects on X are smooth. Moreover, we construct Poisson structures…

In this paper we give some properties of the algebraic and geometric structure of the endomorphisms monoid of a homogeneous vector bundle.

In this paper, we study cohomology groups of vector bundles on neighborhoods of a non-pluriharmonic locus in Stein manifolds and in projective manifolds. By using our results, we show variants of the Lefschetz hyperplane theorem.

Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…

In arXiv:1905.07734 we presented a construction that is an analogue of Pontryagin's for proper maps in stable dimensions. This gives a bijection between the cobordism set of framed embedded compact submanifolds in $W\times\mathbb{R}^n$ for…