2024 Brill noether general curve

Brill noether general curve

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August undefined, 2024

WebJun 1, 2024 · More precisely, in classical Brill-Noether theory, the embedding theorem states that a general linear series of degree d and rank r on a general curve of genus g is an embedding if r is at least 3. 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 ...

BRILL-NOETHER THEORY FOR CURVES OF A FIXED GONALITY

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 … WebJan 28, 2024 · Brill-Noether theory for higher-rank extends naturally to the case of nodal irreducible curves by considering stable torsion free sheaves and their moduli spaces … pure envy bayport ny

Linear Series on a Curve General in - University of Texas at …

WebThe Brill–Noether theorem says that, if Cis a general curve of genus g, this naive dimension count is correct. More precisely, the dimension of Wr d (C) is ˆ(g;r;d) := g (r+ 1)(g d+ r); where a scheme is understood to be empty when its dimension is negative. This result was ﬁrst proved in a seminal paper by Grifﬁths and Harris [27]. 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 … http://homepages.math.uic.edu/~coskun/BrillNoetherK3.pdf section 15 of consumer protection act

Brill–Noether general curves on Knutsen K3 surfaces

Brill-Noether theory and Green

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 … WebConstructing Reducible BN-Curves 1957 Then C1 ∪Γ C2 → Pr is a BN-curve, provided it has nonnegative Brill–Noether number. Furthermore, if both C i → Pr are general in some component of the space of NNS-curves passing through Γ, then C1 ∪Γ C2 → Pr is an interior BN-curve. (Note that if d i = g i +r for both i ∈ {1,2}, the condition that C1 ∪Γ C2 … puree of aubergine and tahiniWebNov 23, 2015 · Explicit Brill-Noether-Petri general curves. Let be the points in with coordinates respectively. We prove that, for any genus , a plane curve of degree having … section 15 of arbitration

"WebBRILL-NOETHER THEORY TONY FENG This article follows the paper of Grifﬁths and Harris, "On the variety of special linear systems on a general algebraic curve." 1. … " - Brill noether general curve

Brill noether general curve

[1511.07321] Explicit Brill-Noether-Petri general curves - arXiv

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 ... WebLinear series are the central object of study in the classical Brill-Noether theory of algebraic curves. For example, the main results of Brill-Noether theory imply that when ˆ(g;r;d) := g (r+ 1)(g d+ r) is nonnegative, the gr d s on a general curve Xof genus gform a proper scheme Gr d (X) that

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WebMay 4, 2024 · Abstract. We 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. … 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 ...

Webof 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 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 …

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. … 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 …

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

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 … puree paint thinner data sheetWebFeb 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 ... section 15 non fatal offencesWebOct 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 … section 15 of cpcWebWhen the Brill–Noether number $\rho $ is zero, we recover the Castelnuovo formula for the number of special linear series on a general curve; when $\rho =1$, 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 ... section 1 5 of esi actWebNov 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 ... puree of mushroom soupWebrank on the general curve in Mg, and complete analogs of the standard Brill-Noether theorems for curves that are general in Hurwitz spaces. Other advances include partial … puree packWebIn 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 … puree owocowe