Brill noether general curve
WebApr 1, 2024 · Abstract. Severi varieties and Brill–Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface S with polarization L of type (1, n), we prove nonemptiness and regularity of the Severi variety parametrizing δ-nodal curves in the linear system L for ... 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 ...
Brill noether general curve
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WebOct 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 … 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.
WebBRILL-NOETHER THEORY, II TONY FENG The discussion in §1 essentially establishes the case d= 3, as we saw that degenerating until two pairs of lines intersected …
Webspecial linear series on a general curve; when ρ = 1, we recover the formulas of Eisenbud-Harris, Pirola, and Chan–Martín–Pflueger–Teixidor for the arithmetic genus of a Brill–Noether curve of special divisors. These computations are obtained as applications of a new determinantal formula for the K-theory class of certain degeneracy loci. 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 Harris states that a general curve has no divisors with negative Brill–Noether number. A curve having no divisors with negative Brill–Noether number is hence ...
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 …
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 … tykhe cardsWebMar 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 ... tan bottega shoesWebNov 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 … tan booties cheapWebFrom 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 … ty kids descargarWebof Curves of Genus 23 GAVRIL FARKAS 1 Introduction The problem of describing the birational geometry of the moduli space M g of complex curves of genus g has a long history. Severi already knew in 1915 that M ... g is of general type as soon as g ≥ 24 and that the Kodaira dimension of M23 is ≥ 1 (see [HM], [EH3]). We note that M tanbridge academy calgaryWebWe 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 … tan booths near meWebWe 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… tyk inschool.fi