Related papers: Remarks on 5-dimensional complete intersections
We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
By analogy with the classical (Chasles-Schubert-Semple-Tyrell) spaces of complete quadrics and complete collineations, we introduce the variety of complete complexes. Its points can be seen as equivalence classes of spectral sequences of a…
It is proved that the number of deformation types of complex structures on a fixed oriented smooth four-manifold can be arbitrarily large. The considered examples are locally simple abelian covers of rational surfaces.
We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…
We prove the "Sullivan Conjecture" on the classification of 4-dimensional complete intersections up to diffeomorphism. Here an $n$-dimensional complete intersection is a smooth complex variety formed by the transverse intersection of $k$…
We prove that a smooth well formed Fano weighted complete intersection of codimension 2 has a nef partition. We discuss applications of this fact to Mirror Symmetry. In particular we list all nef partitions for smooth well formed Fano…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a…
We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the…
A relation between the number of rational curves of fixed degree on Calabi Yau threefolds and the Picard Fuchs equations, which was suggested as part of the study of mirror symmetry, is verified in the case of complete intersection of two…
We describe new explicit examples of moduli spaces of Bridgeland semistable objects on surfaces, parametrizing objects whose numerical class agrees with the class of a point. This follows ideas of Tramel and Xia, using stability conditions…
In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider…
In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…
We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…
In a 1992 paper, Witten gave a formula for the intersection pairings of the moduli space of flat $G$-bundles over an oriented surface, possibly with markings. In this paper, we give a general proof of Witten's formula, for arbitrary…
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
We give examples of open manifolds that carry infinitely many complete metrics of nonnegative sectional curvature such that they all have the same soul, and their isometry classes lie in different connected components of the moduli space.…
We describe the intersection complex of any perversity of a toric variety completely in terms of the associated fan. It is described by a finite complex of finite dimensional graded vector spaces which we call graded exterior modules. The…
Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair. This work finds that there are at most nine such pairs amongst all ten line arrangements…