Brill noether general curve

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August undefined, 2024

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. … 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

Constructing Reducible Brill–NoetherCurves

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 … 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 … flower print rain boots

Brill–Noether theory of curves on toric surfaces - ScienceDirect

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 … 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 … 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 ... flower print out free

The Geometry of the Moduli Space of Curves of Genus 23

Higher-rank Brill-Noether loci on nodal reducible curves

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]. For a given genus g, the moduli space for curves C of genus g should contain a dense subset parameterizing those curves with the minimum in the way of special divisors. One goal of the theory is to 'count constants', for those curves: to predict the dimension of the space of special divisors (up to linear equivalence) of a given degree d, as a function of g, that must be present on a curve of that genus. green and pink crystalsWebNov 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 … flower print outs

"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 general curve

Brill noether general curve

K-classes of Brill–Noether Loci and a Determinantal Formula

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 … 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 ...

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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. 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 ...

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 … 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 … 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 …

WebJun 26, 2024 · general points. While there are known exceptions in low-dimensional projective spaces, we expect: Conjecture 1.1. For all but finitely many tuples (d, g, r), a Brill–Noether curve of degree d and genus g in \({\mathbb {P}}^r\) interpolates through f(d, g, r) general points (and no more).This conjecture has historically attracted significant …

WebWhile these are all subtle questions for an arbitrary curve, when the curve Cis of general moduli, the work of many authors in the 1980s showed that the geometry of Wr d Cis more uniform. Theorem 1 (The Brill{Noether theorem). Let Cbe a general curve of genus g. (Gri ths{Harris [6]) Wr d Cis nonempty if and only if the Brill{Noether number flower print sandals for womenWebFeb 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 ... flower print out picturesWebNov 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 ... flower printouts to colorWebConstructing 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 … flower print outlineWebJan 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 … green and pink emoji combosWebrank 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 … flower printouts for coloringWebApr 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 ... flower print one piece