Related papers: Noncommutative Smooth Models

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about…

The aim of this paper is two--fold. We first strongly improve our previous main result Theorem 3.1 in Arxiv 1702.00918v3 12Feb2018 ("Brill-Noether loci of rank two vector bundles on a general $\nu$-gonal curve"), concerning classification…

In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary…

We relate the Brauer group of a smooth variety over a p-adic field to the geometry of the special fibre of a regular model, using the purity theorem in \'etale cohomology. As an illustration, we describe how the Brauer group of a smooth del…

Given a non-singular variety with a K3 fibration f : X --> S we construct dual fibrations Y --> S by replacing each fibre X_s of f by a two-dimensional moduli space of stable sheaves on X_s. In certain cases we prove that the resulting…

We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth…

We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of the map from the ring of rational…

Let $\pi\cln X\to \Delta^m$ be a proper smooth K\"ahler morphism from a complex manifold $X$ to the unit polydisc $\Delta^m$. Suppose the fibers over the complement of a proper analytic subset are biholomorphic to a fixed projective…

We establish a connection between the representation theory of certain noncommutative singular varieties and two-dimensional lattice models. Specifically, we consider noncommutative biparametric deformations of the fiber product of two…

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is…

In this paper we study noncommutative plane curves, i.e. non-commutative k-algebras for which the 1-dimensional simple modules form a plane curve. We study extensions of simple modules and we try to enlighten the completion problem, i.e.…

We consider recognizable evaluations for a suitable category of oriented two-dimensional cobordisms with corners between finite unions of intervals. We call such cobordisms thin flat surfaces. An evaluation is given by a power series in two…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…

One of the major open problems in noncommutative algebraic geometry is the classification of noncommutative surfaces, and this paper resolves a significant case of this problem. Specifically, let S denote the 3-dimensional Sklyanin algebra…

The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a K\"ahler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A…

Let $X$ be a smooth, irreducible, projective algebraic surface, and let $\alpha \in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $\alpha$-stable coherent…

We prove that the weight-two Hodge structure of moduli spaces of torsion-free sheaves on a K3 surface is as described by Mukai (the rank is arbitrary but we assume the first Chern class is primitive). We prove the moduli space is an…

We study the singularities of the irreducible components of the Springer fiber over a nilpotent element N with N^2=0 in a Lie algebra of type A or D (the so-called two columns case). We use Frobenius splitting techniques to prove that these…