Brill noether general curve
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 … 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 …
Brill noether general curve
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WebJan 8, 2024 · We prove a generalisation of the Brill-Noether theorem for the variety of special divisors W d r ( C) on a general curve C of prescribed gonality. Our main …
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 ... 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 complete intersections in projective space, tend to have divisors with negative Brill-Noether number, and constructing particular curves of high genus having no such divisors …
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 … 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 …
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.
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 … nash county board of elections ncWebNov 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 … member for broadwater queenslandWebWhile 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 member for churchlandsWebOct 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 … nash county assessor ncWebNov 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 … member for cook electorate officeWebThe 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]. nash county boardWebWhen 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 ... nash county board of education nc