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Covering gonality

WebJan 8, 2024 · Then the covering gonality of S is { {\mathrm {cov.gon}}} (S)=d-2, and any family of irreducible curves computing the covering gonality is equivalent to (a subfamily of) one of the families described in Example 3.4 of the original paper. Example Assume that there exist two rational curves R_1,R_2\subset S. WebDec 15, 2024 · The gonality of an algebraic curve defined over a number field is bounded from below by the stable gonality of the intersection dual graph of its reduction modulo any prime ideal of the number field. This makes stable gonality of graphs relevant for number theoretic problems (e.g. [17]).

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WebJan 8, 2024 · Then the covering gonality of S is \({{\mathrm{cov.gon}}}(S)=d-2,\) and any family of irreducible curves computing the covering gonality is equivalent to (a subfamily of) one of the families described in Example 3.4 of the original paper. Example. Assume that there exist two rational curves \(R_1,R_2\subset S\). WebAbstract This thesis is divided into three parts. In the first, we define the covering gonality and separable covering gonality of varieties over fields of positive characteristic, … pit bull rescue washington https://gokcencelik.com

Covering gonalities in positive characteristic Mathematics

Webthat covering gonality four is in fact achieved by an (essentially) unique explicit family of curves and the same for connecting gonality five, which we now describe. Given a line ℓ ⊂ X, one defines the incidence divisor Dℓ ⊂ S parametrising lines is either of first or of second type. The locus of lines of second type for a general WebMay 1, 2024 · Since cov. gon (Y) = 1 is equivalent to Y being uniruled, we can think of the covering gonality as a measure of the failure of Y to be uniruled. The following theorem is probably the most general result governing the gonality of moving curves in a very general hypersurface of large degree. WebThe gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum number of chips that can be placed on that graph such that a debt of 1 can be eliminated via "chip-firing moves" over all possible debt placements. stick fabric to wood

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Category:Gonality of curves on general hypersurfaces - ScienceDirect

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Covering gonality

[2005.08878] Covering gonalities of complete intersections in …

WebNov 28, 2024 · We deduce that, for k at least 3, a very general abelian variety of dimension at least 2k−2 has covering gonality greater than k. This settles a conjecture of Voisin. WebThe gonality conjecture, of M. Green and R. Lazarsfeld, predicts that the gonality of the algebraic curve C can be calculated by homological algebra means, from a minimal resolution of an invertible sheaf of high degree. In many cases the gonality is two more than the Clifford index.

Covering gonality

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WebApr 18, 2015 · According to Kato and Martens (Arch Math 103:111–116, 2014), the gonality sequence of a curve X of genus g which doubly covers a curve Y of genus h > 0 is completely determined by the gonality sequence of the covered curve Y provided that g is sufficiently large w.r.t. h. WebAug 1, 2024 · Covering gonality of symmetric products of curves and Cayley-Bacharach condition on Grassmannians Francesco Bastianelli, Nicola Picoco Given an irreducible …

Webit is from being rational. When n= 1, the natural invariant is the gonality of a curve C, defined to be the smallest degree of a branched covering C′ → P1 (where C′ is the normalization of C). One generalization of gonality to higher dimensions is the degree of irrationality, defined as:

WebFeb 20, 2024 · Chow ring and gonality of general abelian varieties Authors: Claire Voisin Abstract We study the (covering) gonality of abelian varieties and their orbits of zero-cycles for rational... WebMay 1, 2015 · Introduction. Let V be a smooth connected complete curve over C which admits a structure of d -cyclic covering of the projective line P 1 with n branch points. In …

WebAug 1, 2024 · Covering gonality of symmetric products of curves and Cayley-Bacharach condition on Grassmannians Francesco Bastianelli, Nicola Picoco Given an irreducible projective variety , the covering gonality of is the least gonality of an irreducible curve passing through a general point of .

WebJun 3, 2011 · Answering a question posed by Peskine, we show the gonality of C is d l, where d is the degree of the curve and l is the maximum order of a multisecant line of C. … stickey and audi mattressesWebor bounded the covering gonality for specific classes of complex varieties [1, 2, 13, 7]. In this article we study the covering gonality of varieties over arbitrary fields. Definition 1.1. Let X be an irreducible proper variety of dimension n over a field k. The covering gonality of X over k, denoted cvg(X), is the minimal e such that there pitbull rescue tv show based in louisianaWebThe main result in this paper is the following Theorem 1.1, which determines the covering gonality ofa verygeneral hypersurfaceX⊂Pn+1 ofsufficiently large degree and arbitrarydimension, apart from a series of exceptions for which, as we will see, the covering gonality is almost determined (see Remark 1.2 below). Theorem 1.1. pit bull rescue tv showWebJul 9, 2024 · covering gonality, gonality, measures of irrationality, complete intersections Mathematical Subject Classification Primary: 14E08 Secondary: 14C15, 14M10 Milestones Received: 26 June 2024 Revised: 18 April 2024 Accepted: 4 July 2024 Published: 9 July 2024 Authors Geoffrey Smith Department of Mathematics, Statistics, and Computer … stick factory edinburghWebWe define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery for complex varieties. We show that, over an algebraically closed field, a smooth multidegree (d1,…⁡,dk)complete intersection in ℙNhas separable covering stick family of 3WebThis thesis is divided into three parts. In the first, we define the covering gonality and separable covering gonality of varieties over fields of positive characteristic, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a smooth degree d dimension n hypersurface has … pitbull reversedWebexample, the covering gonality of a uniruled manifold is 1, while its irrationality is 1 only if it is rational. One can similarly introduce the “covering genus” covgen(X), namely the genus of a curve C, which is the general fiber of a family ψ: C → B, φ: C → X of curves … pitbull rescues in washington state