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Covering gonality

Webor 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 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 …

arXiv:1511.01359v2 [math.AG] 30 Nov 2016

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]). WebAug 1, 2024 · These include the least degree of a rational covering of projective space, and the minimal gonality of a covering family of curves. The theme is that positivity … farm dog flowers batavia https://baileylicensing.com

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WebWe 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 WebGonality of abelian varieties317 is obtained by a direct generalization of Pirola’s arguments in [Pir89], says that “naturallydefinedsubsets”ofabelianvarieties(seeDefinition2.1),assumingthey arepropersubsetsforverygeneralabelianvarietiesofagivendimensiong,areat … WebWe study various measures of irrationality for hypersurfaces of large degree in projective space and other varieties. These include the least degree of a rational covering of … free online hs diploma

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Covering gonality

Zero-Cycles and Measures of Irrationality for Abelian …

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.

Covering gonality

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WebThe degree of irrationality and the covering gonality measure respectively the failure of $X$ to be rational and uniruled and are thus called measures of irrationality. By studying … WebThe 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.

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, … 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 · In this paper we study the covering gonality of the k -fold symmetric product C ( k ) of a smooth complex projective curve C of genus g ≥ k + 1. It follows from a … WebIn this chapter, we generalize the notion of covering gonality as defined in [6] to varieties defined over arbitrary fields. Recall that for an irreducible projective variety X defined …

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WebTherefore the main issue is bounding the covering gonality from below. In [3], the first author proved that the covering gonality of C(2) equals the gonality of C, i.e. (1.1) is actually an equality, provided that g≥ 3. In this paper, we prove the same for the 3-fold and the 4-fold symmetric product of a curve. Theorem 1.1. free online hspt practice testWebJan 23, 2024 · Besides these notions, there is a growing interest in bounding some quantitative measures of irrationality, e.g. covering gonality and degree of irrationality. These measures have been studied/known for very general hypersurfaces and complete intersections in projective space, K3 surfaces, abelian varieties, etc. free online html5 gamesWebJan 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 \(R_1,R_2\subset S\). free online hse courses