Search results for "covering"
showing 10 items of 61 documents
MR 2918162 Reviewed Van der Geer G. and Kouvidakis A. The Hodge bundle on Hurwitz spaces. Pure and Applied Mathematics Quarterly (2011) 7, no. 4, 129…
2012
In this paper the authors consider the Hurwitz space $H_{g, \, d}$ that parametrizes degree $d$ simple coverings of $\mathbb{P}^{1}$ with $b = 2 g - 2 + 2d$ branch points. The compactification $\bar{H}_{g, \, d}$ of this Hurwitz space is the space of admissible covers of genus $g$ and degree $d$, $f: C \rightarrow P$, where $C$ is a nodal curve and $P$ is a stable $b$-pointed curve of genus $0$. Assigning to $f: C \rightarrow P$ the stabilized model of $C$, one defines a natural map $\phi: \bar{H}_{g, \, d} \rightarrow \bar{M}_{g}$ where $\bar{M}_{g}$ denotes the moduli space of stable curves of genus $g$. The Hurwitz space $\bar{H}_{g, \, d}$ carries a natural $\mathbb{Q}$-divisor class, t…
Dismantling and electrochemical copper recovery from Waste Printed Circuit Boards in H2SO4–CuSO4–NaCl solutions
2019
Abstract The worldwide growing of electrical and electronic equipment makes increasingly urgent to find environmentally friendly treatments for e-waste. In this paper, the attention has been focused on i) the eco-friendly dismantling of the electronic components from Waste Printed Circuit Boards and ii) recovering of pure metallic copper, which is the most abundant metal and one of the most valuable in Printed Circuit Boards. After an experimental optimization study, we found that a solution containing 0.5 M H2SO4, 0.4 M CuSO4, and 4 M NaCl can be successfully used to disassemble the electronic components from the boards by leaching of all exposed metals. Air was blown into the leaching sol…
Quasiregular ellipticity of open and generalized manifolds
2014
We study the existence of geometrically controlled branched covering maps from \(\mathbb R^3\) to open \(3\)-manifolds or to decomposition spaces \(\mathbb {S}^3/G\), and from \(\mathbb {S}^3/G\) to \(\mathbb {S}^3\).
Unirationality of Hurwitz spaces of coverings of degree <= 5
2011
Let $Y$ be a smooth, projective curve of genus $g\geq 1$ over the complex numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings $p:X \to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy group equal to $S_d$, and $det(p_{*}O_X/O_Y)$ isomorphic to a fixed line bundle $A^{-1}$ of degree $-e$. We prove that, when $d=3, 4$ or $5$ and $n$ is sufficiently large (precise bounds are given), these Hurwitz spaces are unirational. If in addition $(e,2)=1$ (when $d=3$), $(e,6)=1$ (when $d=4$) and $(e,10)=1$ (when $d=5$), then these Hurwitz spaces are rational.
2020
Abstract This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a C ∞ -hypersurface S without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure H 12 . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorf…
Modular Calabi-Yau threefolds of level eight
2005
In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle cohomologies should exist between these varieties. In the paper we construct several examples of such correspondences. In the constructions elliptic fibrations play a crucial role. In fact we show that all but three examples are in some sense built upon two modular curves from the Beauville list.
Corrigendum: Unirationality of Hurwitz Spaces of Coverings of Degree ≤5
2017
We correct Proposition 3.12 and Lemma 3.13 of the paper published in Vol. 2013, No.13, pp.3006-3052. The corrections do not affect the other statements of the paper. In this note, we correct a flow in the statement of Proposition 3.12 of [1] which also leads to a modification in the statement of Lemma 3.13 of [1]. We recall that in this proposition one considers morphisms of schemes X ?→π Y ?→q S, where q is proper, flat, with equidimensional fibers of dimension n and π is finite, flat and surjective. Imposing certain conditions on the fibers it is claimed that the loci of s € S fulfilling these conditions are open subsets of S. A missing condition should be added and the correct version of…
A criterion for homeomorphism between closed Haken manifolds
2003
In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.
Hasse diagrams and orbit class spaces
2011
Abstract Let X be a topological space and G be a group of homeomorphisms of X. Let G ˜ be an equivalence relation on X defined by x G ˜ y if the closure of the G-orbit of x is equal to the closure of the G-orbit of y. The quotient space X / G ˜ is called the orbit class space and is endowed with the natural order inherited from the inclusion order of the closure of the classes, so that, if such a space is finite, one can associate with it a Hasse diagram. We show that the converse is also true: any finite Hasse diagram can be realized as the Hasse diagram of an orbit class space built from a dynamical system ( X , G ) where X is a compact space and G is a finitely generated group of homeomo…