相关论文: An explicit formula for a branched covering from $…
We propose a generalization of S-folds to 4d $\mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $\mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a…
We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.
We obtain an explicit formula for the symplectic form over the double quotient with help of the Green function of a Riemann surface.
This paper is a contribution to the study of foliations on $\mathbb{CP}^2$ with a unique singularity. We provide an explicit example in degree 7 of such a foliation, in the non dicritical case, having a divergent separatrix, and…
In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex manifold. Assuming some extra nondegenericity and using the result of Hong, complete…
In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $n$ dimensional manifolds. We show that the local structure of a complex point up to isotopy only depends on their type (either elliptic or…
We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in…
We deduce some formulas for the spin invariants of the connected sum of an arbitrary 4-manifold X, b^+ _2(X) > 0 $ with $\overline {CP^2}$ in terms of the spin invariants of $X$ and apply this to prove the Van de Ven conjecture.
A finite morphism $f:X\to \mathbb P^2$ of a a smooth irreducible projective surface $X$ is called an almost generic cover if for each point $p\in \mathbb P^2$ the fibre $f^{-1}(p)$ is supported at least on $deg(f)-2$ distinct points and $f$…
We compute the canonical model of the cover of Shimura curves $X_0(2) \to X(1)$ for the cubic field of discriminant 13^2 described at the end of Elkies' paper "Shimura curves for level 3 subgroups of the (2,3,7) triangle group". Last, we…
A cyclic cover over the Riemann sphere branched at four points inherits a natural flat structure from the "pillow" flat structure on the basic sphere. We give an explicit formula for all individual Lyapunov exponents of the Hodge bundle…
In this paper, we first prove that any closed simply connected 4-manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4-manifolds: $\mathbb{S}^4$,…
We propose an approach for the computation of multi-parameter families of Galois extensions with prescribed ramification type. More precisely, we combine existing deformation and interpolation techniques with recently developed strong tools…
We study branched covering spaces in several contexts, proving that under suitable circumstances the cover satisfies the same upper curvature bounds as the base space. The first context is of a branched cover of an arbitrary metric space…
A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links without changing the represented manifold. That is, we…
For any $n>1$, we construct examples branched Galois coverings from $M$ to the nth projective space ${\mathbb P}^n$ where $M$ is one of $({\mathbb P}^1)^n$, ${\mathbb C}^n$ or $(B_1)^n$, and $B_1$ is the 1-ball. In terms of orbifolds, this…
A formula for factorizations of the full twist in the braid group $Br_{2m}$ depending on any four factorizations of the full twist in $Br_{m}$ is given. Applying this formula, a symplectic 4-manifold $X$ and two isotopic generic coverings…
We give a formula to compare the Quillen metrics associated to a branched covering from holomorphic line bundles.
We introduce the concept of a covering of a graded pointed Hopf algebra. The theory developed shows that coverings of a bosonized Nichols algebra can be concretely expressed by biproducts using a quotient of the universal coalgebra covering…
Let $\widetilde{G}$ be the $n$-fold covering group of the special linear group of degree two, over a non-Archimedean local field. We determine the decomposition into irreducibles of the restriction of the principal series representations of…