Related papers: PU(2) Monopoles, I: Regularity, Uhlenbeck Compactn…

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat K\"ahler ALE metrics with negative mass, on the…

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is…

We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual…

We review warped compactifications of superstring theory with some attention to the limit in which these resemble "bottom-up" phenomenological models. In addition to some discussion of the original Klebanov-Witten and Klebanov-Strassler…

Using the standard Cayley transform and elementary tools it is reiterated that the conformal compactification of the Minkowski space involves not only the "cone at infinity" but also the 2-sphere that is at the base of this cone. We…

We study moduli stabilization in 4D effective field theories with Sp(4,$\mathbb{Z}$) self-duality inspired by heterotic orbifold compactifications with Wilson lines. The target-space duality group of these theories is enhanced from…

We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality…

We show that two properly embedded compact surfaces in an orientable 4-manifold are cobordant if and only if they are $\mathbb{Z}/2$-homologous and either the 4-manifold has boundary or the surfaces have the same normal Euler number. If the…

The duality symmetry group of the cosets ${\textstyle SU(n,1)\over \textstyle SU(n)\otimes U(1)}$, which describe the moduli space of a two-dimensional subspace of an orbifold model with $(n-1)$ complex Wilson lines moduli, is discussed.…

This paper discusses the dilaton, K\"ahler moduli and hidden sector matter chiral superfields of heterotic $M$-theory vacua in which the hidden sector gauge bundle is chosen to be a line bundle with an anomalous U(1) structure group. For…

We consider interesting Seiberg dualities for $Usp$ gauge theories with an antisymmetric, $8$ fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses,…

The Satake compactification of the moduli space of principally polarized abelian surfaces with a level two structure has a degree 8 endomorphism. The aim of this paper is to show that this result can be extended to other modular threefolds.…

We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $\IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper…

We exhibit examples of closed Riemannian 7-manifolds with holonomy G_2 such that the underlying manifolds are diffeomorphic but whose associated G_2-structures are not homotopic. This is achieved by defining two invariants of certain…

We prove that any class $VII$ surface with $b_2=1$ has curves. This implies the "Global Spherical Shell conjecture" in the case $b_2=1$: Any minimal class $VII$ surface with $b_2=1$ admits a global spherical shell, hence it is isomorphic to…

The introduction of a modulus z(K), analogous to u=<tr phi^2> in the N=2 SUSY SU(2) gauge theory solved by Seiberg and Witten, and whose defining property is the invariance under the symmetry and duality transformations of the effective…

This article explores solutions to a generalised form of the Seiberg--Witten equations in higher dimensions, first introduced by Fine and the author. Starting with an oriented $n$ dimensional Riemannian manifold with a…

This work is a sequel to our previous monograph arXiv:2010.15789 (to appear in AMS Memoirs), where we initiated our program to prove that the Bogomolov-Miyaoka-Yau inequality holds for closed, symplectic four-manifolds and, more generally,…

We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\Sigma \times \Sigma$ where $\Sigma$ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type…

The recent proof by Madsen and Weiss of Mumford's conjecture on the stable cohomology of moduli spaces of Riemann surfaces, was a dramatic example of an important stability theorem about the topology of moduli spaces. In this article we…