Search results for "Geometria"
showing 10 items of 422 documents
Irreducibility of Hurwitz spaces of coverings with monodromy groups Weyl groups of type W(B_d)
2007
Let Y be a smooth, connected, projective complex curve of genus ≥0. R. Biggers and M. Fried [J. Reine Angew. Math. 335, 87–121 (1982; Zbl 0484.14002), Trans. Am. Math. Soc. 295, No. 1, 59–70 (1986; Zbl 0601.14022)] proved the irreducibility of the Hurwitz spaces which parametrize coverings of ℙ 1 whose monodromy group is a Weyl of type W(D d ). Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type W(B d ).
On coverings with special points and monodromy group a Weyl group of type B_d
2014
In this paper we study Hurwitz spaces parameterizing coverings with special points and with monodromy group a Weyl group of type Bd. We prove that such spaces are irreducible if k > 3d ? 3. Here, k denotes the number of local monodromies that are reflections relative to long roots.
On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points
2013
In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.
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…
MR 2834249 Reviewed Hoshi Y., Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero, Nagoya…
2013
Let K be a finitely generated field of characteristic zero, l be a prime number and S be a scheme. In this paper, the author studies isomorphism classes of hyperbolic curves. The author calls the pair (C, D), where C is a scheme over S and D \subset C is a closed subscheme of C, a hyperbolic curve of type (g, r) over S if C is smooth and proper over S, if any geometric fiber of C \rightarrow S is a connected curve of genus g and if the composite D \rightarrow C \rightarrow S is a finite \'{e}tale covering over S of degree r. The main result of this paper is that the isomorphism class of a hyperbolic curve of genus zero over K that is l-monodromically full is completely determinated by the k…
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…
Steiner configurations ideals: Containment and colouring
2021
Given a homogeneous ideal I&sube
Some families of big and stable bundles on $K3$ surfaces and on their Hilbert schemes of points
2021
Here we investigate meaningful families of vector bundles on a very general polarized $K3$ surface $(X,H)$ and on the corresponding Hyper--Kaehler variety given by the Hilbert scheme of points $X^{[k]}:= {\rm Hilb}^k(X)$, for any integer $k \geqslant 2$. In particular, we prove results concerning bigness and stability of such bundles. First, we give conditions on integers $n$ such that the twist of the tangent bundle of $X$ by the line bundle $nH$ is big and stable on~$X$; we then prove a similar result for a natural twist of the tangent bundle of $X^{[k]}$. Next, we prove global generation, bigness and stability results for tautological bundles on $X^{[k]}$ arising either from line bundles…
A common extension of Arhangel'skii's Theorem and the Hajnal-Juhasz inequality
2019
AbstractWe present a result about $G_{\unicode[STIX]{x1D6FF}}$ covers of a Hausdorff space that implies various known cardinal inequalities, including the following two fundamental results in the theory of cardinal invariants in topology: $|X|\leqslant 2^{L(X)\unicode[STIX]{x1D712}(X)}$ (Arhangel’skiĭ) and $|X|\leqslant 2^{c(X)\unicode[STIX]{x1D712}(X)}$ (Hajnal–Juhász). This solves a question that goes back to Bell, Ginsburg and Woods’s 1978 paper (M. Bell, J.N. Ginsburg and R.G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79(1978), 37–45) and is mentioned in Hodel’s survey on Arhangel’skiĭ’s Theorem (R. Hodel, Arhangel’skii’s so…