Covering gonality

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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 … 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 gonalities of complete intersections in positive …

WebCovering gonality of symmetric products of curves and Cayley-Bacharach condition on Grassmannians Preprint Aug 2024 Francesco Bastianelli Nicola Picoco Given an irreducible projective variety... WebOur ﬁrst results concern covering gonality. Theorem A. Let X ⊆ Pn+1 be a smooth hypersurface of dimension n and degree d ≥ n+2. Then cov.gon(X) ≥ d−n. More generally, we show that v(X) ≥ d − n. Observe that one recovers in particular the lower bound (2) of Bastianelli, Cortini and De Poi on the degree of irrationality of such ... envision imaging in frisco tx

Measures of irrationality for hypersurfaces of large degree

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 18, 2024 · Covering gonalities of complete intersections in positive characteristic Geoffrey Smith We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. envision imaging of north fort worth

KNOW THE DIFFERENCE BETWEEN COVER & CONCEALMENT

[PDF] Covering gonality of symmetric products of curves …

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. WebThis 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 … envision imaging of allen txWebAug 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 … envisioning an english empire

"Webexample, 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 … " - Covering gonality

Covering gonality

Algebra & Number Theory Vol. 16, No. 3, 2024 - MSP

WebWe study the (covering) gonality of abelian varieties and their orbits of zero-cycles for rational equivalence. We show that any orbit for rational equivalence of zero-cycles of degree $k$ has… Expand 15 PDF Save Alert Chern-Dold character in complex cobordisms and theta divisors V. Buchstaber, A. Veselov Mathematics 2024 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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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. WebAug 1, 2024 · Covering gonality of symmetric products of curves and Cayley-Bacharach condition on Grassmannians Francesco Bastianelli, Nicola Picoco Given an irreducible …

WebOct 7, 2024 · “Cover” is anything that can protect you from an incoming projectile, either by stopping it or deflecting it. Most types of cover will also provide you with concealment. … 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]).

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 WebJan 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.

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.

WebJan 24, 2024 · The covering gonality of an irreducible projective variety over the complex numbers is the minimum gonality of a curve through a general point on … dr huseby laguna hills caWebJan 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 $R_1,R_2\subset S$. dr husel chargesWebGonality of abelian varieties317 is obtained by a direct generalization of Pirola’s arguments in [Pir89], says that “naturallydeﬁnedsubsets”ofabelianvarieties(seeDeﬁnition2.1),assumingthey arepropersubsetsforverygeneralabelianvarietiesofagivendimensiong,areat … dr husel trial youtubeWebMay 18, 2024 · Download Citation Covering gonalities of complete intersections in positive characteristic We define the covering gonality and separable covering gonality of … dr huser iii weatherford okWebThe 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. dr husam balkhy of chicagoWebJul 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 … envisioning an empowered nation book reviewWebit 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: envisioning india 2047 upsc