2024 Brill noether general curve

Brill noether general curve

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August undefined, 2024

WebA general Du Val curve C ⊂S satisﬁes the Brill-Noether-Petri Theorem. This, on the one hand, gives a strong indication that the result in [1] is the best possible. On the other … WebThen X is Brill–Noether general. Such curves exist over any complete,discretely valued ﬁeld [2, Appendix B], and the existence of Brill–Noether general curves over an …

BRILL-NOETHER THEORY FOR CURVES OF A FIXED GONALITY

WebThis is the gonality of a general curve of genus 6and in this case Theorem A recovers the Brill-Noether theorem. At the other extreme, the minimum possible gonality of a positive genus curve is := 2, in which case the curve is hyperelliptic. Here, Theorem A shows that dim,A 3(˘) = 3− 2A. This follows from the fact that every 6A WebGeneral relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local ... Curves The Brill And Noether Way Univer, as one of the most working sellers. 13 here will agreed be in the course of the best options to review. cheshire therapy centre warrington

Introduction - University of Illinois Chicago

http://homepages.math.uic.edu/~coskun/BrillNoetherK3.pdf WebJul 1, 2015 · The Brill–Noether number ρ ( g, d, r) associated to D is then defined by the equation ρ ( g, d, r) = g − ( r + 1) ( g − d + r). The Brill–Noether Theorem of Griffiths and … WebConstructing reducible Brill-Noether curves Doc. Math. 27, 1953-1983 (2024) DOI: 10.25537/dm.2024v27.1953-1983. Communicated by Gavril Farkas. Summary. A fundamental problem in the theory of algebraic curves in projective space is to understand which reducible curves arise as limits of smooth curves of general moduli. Special … good manufacturing practice 日本語

BRILL-NOETHER THEORY FOR CURVES OF A FIXED GONALITY

Brill–Noether theory of curves on toric surfaces - ScienceDirect

WebNov 23, 2015 · Explicit Brill-Noether-Petri general curves. Enrico Arbarello, Andrea Bruno, Gavril Farkas, Giulia Saccà. Let be the points in with coordinates respectively. We prove that, for any genus , a plane curve of degree having a -tuple point at , and a -tuple point at , and no other singularities, exists and is a Brill-Noether general curve of genus ... WebBrill{Noether theory studies the geometry of the space Wr d (X) of all degree dembeddings of Xinto Pr. For an arbitrary genus gcurve, Wr d (X) can exhibit pathological properties. … good manufacturing practice 中文WebMar 29, 2016 · When C is a general curve of genus g, the Brill-Noether theorem says that The Brill-Noether theorem fails for special curves, notably curves of low gonality (see [2][3][4][8][9] [10]). As a first ... cheshire therapy

"WebNov 1, 1998 · In this paper we will study the Brill–Noether theory of vector bundles on a smooth projective curve X. As usual in papers on this topic we are mainly interested in stable or at least semistable bundles. Let Wkr, d(X) be the scheme of all stable vector bundles E on X with rank (E)=r, deg (E)=d and h0(X, E)[ges ]k+1. For a survey of the … " - Brill noether general curve

Brill noether general curve

Constructing Reducible Brill–NoetherCurves

WebWe show that a general curve in an explicit class of what we call Du Val pointed curves satisfies the Brill-Noether Theorem for pointed curves. Furthermore, we prove that a generic pencil of Du Val pointed curves is di… WebFeb 1, 2014 · A theorem of Lazarsfeldʼs (see [4]) says that if S is a smooth K3 surface all of whose hyperplane sections are irreducible and reduced, then a general …

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WebFeb 14, 2024 · Kaelin Cook-Powell, University of Kentucky. Title: Improvements to the Brill-Noether Theorem. Abstract: In 1980 Griffiths and Harris proved what is known as the "Brill-Noether Theorem," which essentially says that for a general curve C of genus g that the dimension of a variety of special linear series on C is precisely equal to the Brill ... WebThe study of special divisors on a general curve has traditionally centered around degeneration arguments. One of the first results in this area was due to Griffiths and Harris [7], who proved the assertion of Brill and Noether that if C is a general curve of genus g, then dimWJ(C) = ρ(r, d, g) provided that p(r, d, g) ^ 0. Their method was to ...

WebFrom this theorem follows immediately that on a general curve no divisor has negative Brill-Noether number. Despite this, many curves that are easy to describe, such as … WebAbstract. In this paper we study the Brill-Noether theory of invertible subsheaves of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with hyperplane sections isomorphic to C. Most of our results are based on degeneration ...

WebOct 30, 2024 · Breakthroughs include the proof of the Maximal Rank Theorem, which determines the Hilbert function of the general linear series of given degree and rank on … WebOct 6, 2024 · When the curve C is general, the moduli space of such maps is well-understood by the main theorems of Brill--Noether theory. However, in nature, curves C are often encountered already equipped with a map to some projective space, which may force them to be special in moduli. The simplest case is when C is general among …

WebSep 4, 2024 · We explicitly construct Brill–Noether general K3 surfaces of genus 4, 6 and 8 having the maximal number of elliptic pencils of degrees 3, 4 and 5, respectively, and study their moduli spaces and moduli maps to the moduli space of curves.As an application we prove the existence of Brill–Noether general K3 surfaces of genus 4 and 6 without …

WebBrill-Noether-Petri (BNP) general. i.e. ∀line bundle L on C, the Petri map ... Let C be a BNP general curve of genus g ≥12, then C is the hyperplane section of a K3 surface (or a limit of such) ⇔ the Gauss-Wahl map ν is non-surjective. … good manufacturing practices training coursesWebOct 30, 2024 · Recent Developments in Brill-Noether Theory. David Jensen, Sam Payne. We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations. Breakthroughs include the proof of the … good manufacturing practice 翻译WebJan 23, 2024 · We prove his conjecture, that this upper bound is achieved for a general curve. Our methods introduce logarithmic stable maps as a systematic tool in Brill … good manufacturing practice trainingWebMay 31, 2024 · Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces. Federico Moretti. In this paper we compute the gonality and the … good manufacturing practice 意味WebWe prove a generalisation of the Brill-Noether theorem for the variety of special divisors ,A 3 (˘) on a general curve C of prescribed gonality. Our main theorem gives a closed … good manufacturing practice training courseWebIn calculating the dimensions of such things as C r d and W r d one problem one runs into is that the dimension r (D) (the dimension of the complete linear series of D) is no … good manufacturing practice とはWeb0 fails weak Brill-Noether. Consequently, parts (2) and (4) of Theorem1.1 are sharp. In Section9, we classify the boundary cases in Theorem1.1. In Theorems9.9and9.11, we classify the Mukai vectors v pr;dH;aqwith n€r⁄3nsuch that v fails weak Brill-Noether and we compute the cohomology of the general sheaf for these v. good manufacturing practice بالعربي