Related papers: Instanton bundles on $\mathbb{P}^1\times\mathbb{F}…

This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth…

We present a classification of SU(2) instantons on $T^2\times\mathbb{R}^2$ according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the…

For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector…

This is the revised version of our previous preprint. In this paper, we establish a generic smoothness result for moduli space of semistable sheaves of arbitrary rank over surfaces provided that the second Chern class of the sheaves is…

Let $X$ be a Fano threefold with index $i_X$ and fundamental line bundle $\mathcal O_X(h)$. We classify $\mu$-semistable rank two bundles $\mathcal E$ on $X$ with $c_1(\mathcal E)=0$, $h^0(\mathcal E) \ne 0$ and $h^1(\mathcal…

It has been proved by various authors that a normalized, 1-Buchsbaum rank 2 vector bundle on P3 is a nullcorrelation bundle, while a normalized, 2-Buchsbaum rank 2 vector bundle on P3 is an instanton bundle of charge 2. We find that the…

The construction of Atiyah, Drinfeld, Hitchin, and Manin [ADHM78] provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds…

Tikhomirov (2009) proved the irreducibility of the moduli space of mathematical instantons on the projective 3-space for all odd charges. The irreducibility for charges between 1 and 5 was known before. In the present paper, the rationality…

We determine generators of the rational cohomology algebras of moduli spaces of parabolic vector bundles on a curve, under some `primality' conditions on the parabolic datum. These generators are canonical in a precise sense. Our results…

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 describe a new class of instanton effects in string compactifications that preserve only N=1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective…

Recently, multiple fractional instanton configurations with zero instanton charge, called bions, have been revealed to play important roles in quantum field theories on compactified spacetime. In two dimensions, fractional instantons and…

We prove that the $\ell$-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$-adic…

We employ the ADHM method to derive the moduli space of two instantons in U(1) gauge theory on a noncommutative space. We show by an explicit hyperK\"ahler quotient construction that the relative metric of the moduli space of two instantons…

In previous work, the second author defined 'equivariant instanton homology groups' $I^\bullet(Y,\pi;R)$ for a rational homology 3-sphere $Y$, a set of auxiliary data $\pi$, and a PID $R$. These objects are modules over the cohomology ring…

We describe explicitly the moduli spaces $M^{pst}_g(S,E)$ of polystable holomorphic structures $E$ with $\det E\cong K$ on a rank 2 vector bundle $E$ with $c_1(E)=c_1(K)$ and $c_2(E)=0$ for all minimal class VII surfaces $S$ with $b_2(S)=1$…

We classify globally generated vector bundles on $\mathbf{P}^1 \times \mathbf{P}^1 \times \mathbf{P}^1$ with small first Chern class, i.e. $c_1= (a_1, a_2, a_3)$, $a_i \le 2$. Our main method is to investigate the associated smooth curves…

Let Sigma be a smooth complex curve, and let S be the product ruled surface Sigma \times CP^1. We prove a correspondence conjectured by Donaldson between finite energy U(2)-instantons over the cylinder Sigma \times S^1 \times R, and rank 2…

ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any del Pezzo surface $X$ of degree less or equal than six and…

We classify rank two vector bundles on a Fano threefold of Picard rank one whose projectivizations are weak Fano. We also prove the existence of examples for each case of the classification result. Our classification includes detailed…