Related papers: K-theoretic Donaldson invariants via instanton cou…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

We consider the refined $\mathrm{SU}(r)$ Vafa-Witten partition function of a smooth projective surface with non-zero holomorphic 2-form. This partition function has a vertical contribution, expressible in terms of nested Hilbert schemes.…

This paper, the last in a series of three, studies vector bundles on an elliptic surface whose determinant has odd intersection number with a general fiber and uses this study to calculate certain coefficients of Donaldson polynomials.

Generalized Donaldson-Thomas invariants corresponding to local D6-D2-D0 configurations are defined applying the formalism of Joyce and Song to ADHM sheaves on curves. A wallcrossing formula for invariants of D6-rank two is proven and shown…

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…

We analyse the vector bundle moduli arising from generic heterotic compactifications from the point of view of quiver representations. Phenomena such as stability walls, crossing between chambers of supersymmetry, splitting of non-Abelian…

On certain M-theory backgrounds which are a circle fibration over a smooth Calabi-Yau, the quantum theory of M2 branes can be studied in terms of the K-theoretic Donaldson-Thomas theory on the threefold. We extend this relation to…

Let $P(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal K\"ahler metric on the ruled manifold $P(E)$ in terms of relative K-polystability and the…

We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong…

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with…

Given a quiver with potential associated to a toric Calabi-Yau threefold, the numerical Donaldson-Thomas invariants for the moduli space of framed representations can be computed by using toric localization, which reduces the problem to the…

Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the…

We develope $\mathbb{C}^{\ast}$-equivariant categorical Donaldson-Thomas theory for local surfaces, i.e. the total spaces of canonical line bundles on smooth projective surfaces. We introduce $\mathbb{C}^{\ast}$-equivariant DT categories…

Let $H$ be a semisimple algebraic group. We prove the semistable reduction theorem for $\mu$--semistable principal $H$--bundles over a {\it smooth projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth projective…

This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties.…

A factorization formula for certain automorphisms of a Poisson algebra associated to a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing…

The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via ideal sheaves. Another counting invariant via stable pairs is introduced by Pandharipande and Thomas, which counts pairs of curves and divisors on them.…

Let $X$ be a compact Hermitian surface, and $g$ be any fixed Gauduchon metric on $X$. Let $E$ be an Hermitian holomorphic vector bundle over $X$. On the bundle $E$, Donaldson's heat flow is gauge equivalent to a flow of holomorphic…

We consider Donaldson-Witten theory on four-manifolds of the form $X=Y \times {\bf S}^1$ where $Y$ is a compact three-manifold. We show that there are interesting relations between the four-dimensional Donaldson invariants of $X$ and…

We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…