In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve. We also propose that the mirror reflection of the noncommutative complex torus is the mirror reflection of the elliptic curve together with a linear foliation...

In this article we examine some points in the moduli space of M-Theory at which there arise enhanced gauge symmetries. In particular, we examine the “trivial” points of enhanced gauge symmetry in the moduli space of M-Theory on S × S1/Z2 as well as the points of enhanced gauge symmetry in the moduli space of M-Theory on K3 and those in the moduli space of M-Theory on T 5/Z2 × S. Also, we employ...

In a recent paper [4] we obtained explicit examples of twistor spaces that are associated to a compact self-dual four-manifold admitting a Killing field, and also determined their moduli space. In this note we investigate minitwistor spaces associated to these twistor spaces. We determine their structures, minitwistor lines and also their moduli space. In particular, we show that the moduli spa...

We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang–Mills equations on R discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at each point. We explicitly find the subgroup of the symmetry group that preserves the one-ins...

We introduce the notion of an adequate moduli space. The theory of adequate moduli spaces provides a framework for studying algebraic spaces which geometrically approximate algebraic stacks with reductive stabilizers in characteristic p. The definition of an adequate moduli space generalizes the existing notion of a good moduli space to characteristic p (and mixed characteristic). The most impo...

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor–Wood type inequality. Our main result is a count of the number of connected components of the mod...

This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the “simple type” condition of Donaldson theory. The presentation is intended to complement [GS], presenting the essential ideas rather than the analytical details. It is shown that the boundary region of moduli space contributes 6/64 of ...

In [M], Mainò constructed a moduli space for enriched stable curves, by blowing-up the moduli space of Deligne-Mumford stable curves. We introduce enriched spin curves, showing that a parameter space for these objects is obtained by blowing-up the moduli space of spin curves.

In this paper we study the topology of moduli spaces of tropical curves of genus g with n marked points. We view the moduli spaces as being embedded in a larger space, which we call the moduli space of metric graphs with n marked points. We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In the rest of the pap...