Related papers: Stable reduction of three point covers
We determine the stable reduction at $p$ of all three point covers of the projective line with Galois group ${\rm SL}_2(p)$. As a special case, we recover the results of Deligne and Rapoport on the reduction of the modular curves $X_0(p)$…
We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. The reduction is determined by a hypergeometric…
In this paper we study the reduction of Galois covers of curves, from characteristic 0 to characteristic p. The starting point is a is a recent result of Raynaud which gives a criterion for good reduction for covers of the projective line…
In this paper, we provide a comprehensive solution to the open problem regarding the existence of a recurrence formula for computing fixed points of the Josephus function precisely when the reduction constant is three. Incorporating this…
R. Coleman and K. McMurdy compute the stable reduction of $X_0(p^3).$ On the basis of their ideas, we compute the stable reduction of $X_0(p^4).$ As a result, in the stable reduction of $X_0(p^4)$, we find irreducible components, defined by…
The notes contain a streamlined account on stability of univariate polynomials and related problems
We show the properness of the moduli stack of stable surfaces over $\mathbb{Z}[1/30]$, assuming the locally-stable reduction conjecture for stable surfaces. This relies on a local Kawamata--Viehweg vanishing theorem for for 3-dimensional…
The stable pairs theory of local curves in 3-folds (equivariant with respect to the scaling 2-torus) is studied with stationary descendent insertions. Reduction rules are found to lower descendents when higher than the degree. Factorization…
In this paper we study constant angle surfaces in Euclidean 3-space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the…
In these lecture notes we review different aspects of the arithmetic of K3 surfaces. Topics include rational points, Picard number and Tate conjecture, zeta functions and modularity.
We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.
The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this…
We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo…
Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended…
We construct a stable formal model of a Lubin-Tate curve with level three, and study the action of a Weil group and a division algebra on its stable reduction. Further, we study a structure of cohomology of the Lubin-Tate curve. Our study…
We have examined the stability of triangular equilibrium points in Robes's generalised restricted three body problem. The problem is generalised in the sense that more massive primary has been taken as an oblate spheroid. We have found the…
In this paper, we are concerned with the study of the existence of fixed points for single and multi-valued three-points contractions. Namely, we first introduce a new class of single-valued mappings defined on a metric space equipped with…
The structure of the renormalization-group flows in a model with three quartic coupling constants is studied within the $\epsilon$-expansion method up to three-loop order. Twofold degeneracy of the eigenvalue exponents for the…
We give some explicit calculations for stable distributions and convergence to them, mainly based on less explicit results in Feller (1971). The main purpose is to provide ourselves with easy reference to explicit formulas and examples.…
In this paper, we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p. Our techniques involve related computations in the case of three branch…