2024 Brill noether general curve

Brill noether general curve

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August undefined, 2024

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 ... Websions of Brill-Noether loci of algebraic curves by a specialization inequality. 1. Introduction ... graph of the special ﬁber is such a loop of loops is Brill-Noether general. This is because a genus 4 curve that is not Brill-Noether general must be hyperelliptic, and hence, by Baker’s Specialization Lemma [Bak08], the dual graph of its ...

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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 … 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 … phillys cheese

Brill-Noether theory over the Hurwitz space - University of …

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 ... 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 … 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. … tsb west bridgford

BRILL-NOETHER THEORY

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 … 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 … philly school district benefitsFor 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. tsb westgate road

"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 … " - Brill noether general curve

Brill noether general curve

WebMay 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 … 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. …

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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 … 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 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 …

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 WebNov 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 …

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.

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. … philly schedule baseballWebApr 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 ... philly school district loginWebBRILL-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 … philly schlaflyWebJun 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 … philly school district budgetWebWhile 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 philly schedule nbaWebWhen 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 ... tsb weston favell addressWebIn 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 … philly scholarships