相关论文: An explicit formula for a branched covering from $…

We consider $d=2$, $\mathcal{N}=(0,2)$ SCFTs that can arise from M5-branes wrapping four-dimensional, complex, toric manifolds and orbifolds. We use equivariant localization to compute the off-shell central charge of the dual supergravity…

Exact bounds for the positions of the branch points for cyclic coverings of the $p$-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato's *-trees, and secondly by giving explicit matrix…

A topological invariant of a polynomial map $p:X\to B$ from a complex surface containing a curve $C\subset X$ to a one-dimensional base is given by a rational second homology class in the compactification of the moduli space of genus $g$…

In this paper we examine the structure of complex points of real 4-manifolds embedded into complex 3-manifolds up to isotopy. We show that there are only two types of complex points up to isotopy and as a consequence, show that any such…

We study the stratification of the singular locus of four dimensional $\mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant…

We explore the $\mathbb{Z}_{2,3,4,6}$ S-foldings of some 5d superconformal field theories from the $(p,q)$ 5-brane web perspective. The S-folding involves both a spatial quotient and an $\mathrm{SL}(2,\mathbb{Z})$ transformation on 5-branes…

We prove two results about degree of polynomial mappings of $C^2$ to $C^2$.

We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines branched at 4 points and obtain…

A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its polynomials are not greater than three. In…

We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…

This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, $S^2(2,4,4)$ cannot be the cusp cross-section of any orbifold quotient…

Branched covering have a long history from ramification of Riemann surfaces to realization of 3-manifolds as covering ramified over a knots; from geometrical topology to algebraic geometry. The present work investigates a notion of branched…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…

Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2,…

Suppose $k$ is an algebraically closed field of characteristic two, let $A_4$ be an alternating group on four letters, and let $H$ be the unique Sylow two-subgroup of $A_4$. Let $X$ be a smooth projective irreducible curve over $k$ with a…

For the existence of a branched covering Sigma~ --> Sigma between closed surfaces there are easy necessary conditions in terms of chi(Sigma~), chi(Sigma), orientability, the total degree, and the local degrees at the branching points. A…

We generalize the multiple cover formula of Y. Toda (proved by Maulik-Thomas) for counting invariants for semistable coherent sheaves on local K3 surfaces to semistable twisted sheaves over twisted local K3 surfaces. The formula has an…

We show that $\mathbb{C}^2$ contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of $\mathbb{C}^2$. The construction is based on realizing corks as branched covers of…

In this paper we describe what should perhaps be called a `type-2' Vassiliev invariant of knots S^2 -> S^4. We give a formula for an invariant of 2-knots, taking values in Z_2 that can be computed in terms of the double-point diagram of the…

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…