相关论文: Canonical singularities of orders over surfaces

We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.

We introduce the notion of a zebra structure on a surface, which is a more general geometric structure than a translation structure or a dilation structure that still gives a directional foliation of every slope. We are concerned with the…

We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…

We prove semi-rationalification and semi-log-canonicalization for Gorenstein demi-normal surfaces. That is, given a Gorenstein demi-normal surface X with semi-rational (respectively, semi-log canonical) singularities in an open set U with…

We characterize property $(N_p)$ on a polarized surface $(X,L)$ with trivial canonical bundle in terms of the (non)existence of certain forbidden subvarieties of $X$.

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…

We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.

In this note we construct an unlimited family of irregular algebraic surfaces of general type with canonical map of degree $ 8 $, irregularity $ 1 $ and arbitrarily large geometric genus such that the image of the canonical map is not a…

A new approach for treating boundary Poisson structures based on causality and locality analysis is proposed for a single scalar field with boundary interaction. For the case of linear boundary condition, it is shown that the usual…

The periodic cyclic homology of any proper dg category comes equipped with a canonical pairing. We show that in the case of the dg category of matrix factorizations of an isolated singularity the canonical pairing can be identified with the…

We introduce the notions of the caustic-equivalence and the weak caustic-equivalence relations of reticular Lagrangian maps in order to give a generic classification of caustics on a corner. We give the figures of all generic caustics on a…

In this article we consider exceptional sequences of invertible sheaves on smooth complete rational surfaces. We show that to every such sequence one can associate a smooth complete toric surface in a canonical way. We use this structural…

We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…

We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant…

We discuss some "folklore" results on categorical crepant resolutions for varieties with quotient singularities.

On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…

The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of the interest in these classifications is that it enables…

We study holomorphic locally homogeneous geometric structures modelled on line bundles over the projective line. We classify these structures on primary Hopf surfaces. We write out the developing map and holonomy morphism of each of these…

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…

We construct the canonical structure of an irreducible projective variety on the set of connected curves of degree $d$ in $\Bbb P^n$ with rational components (some components can be multiple). The set of rational curves is open subset in…