Hurwitz formula reducible curve
Web1 okt. 2024 · By the Hurwitz formula for any cyclic cover p: C ˜ → C (which is unramified by definition), the genus of C ˜ will be g ˜ = n (g − 1) + 1, if the genus of C is g. From now on, we keep this relation between g ˜, g, n fixed and we use only g, n as the free variables in our problem. There is a bijection between cyclic covers and level n curves. WebBy the Riemann-Hurwitz formula, these are related by the equation b= 2d+2g 2. Consequently, we will construct a scheme Hd;bthat parameterizes simple d-sheeted …
Hurwitz formula reducible curve
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Web29 dec. 2015 · By convention, when we present a hyperelliptic curve as y 2 = h ( x), we are resolving any singularities. Since birational nonsingular curves are isomorphic, this resolution, X ^, is unique. Furthermore, the projection ( x, y) ↦ y from X onto A 1 lifts uniquely to a map X ^ → P 1. Now we look at the projectivization. http://www.columbia.edu/~abb2190/RH.pdf
Web1 jan. 2011 · To the study of such questions of importance are questions about reducibility of the curve f 1 (x)g 2 (y) − f 2 (x)g 1 (y) = 0, where f = f 1 / f 2 , g = g 1 /g 2 , and f 1 , f 2 , as well as g 1... WebHurwitz gave a simple formula when g= 0 (for any , [H]); his result was largely forgotten until recently. (Strehl has extended Hurwitz’s idea to a complete proof, [St].) Let l( ) be …
Web23 jul. 2024 · The relative Riemann–Hurwitz formula July 2024 DOI: 10.1080/00927872.2024.1968886 Authors: Zhiguo Ding Michael E. Zieve Abstract For … WebAbstract. For any nonconstant f, g ∈ C ( x) such that the numerator H ( x, y) of f ( x) − g ( y) is irreducible, we compute the genus of the normalization of the curve H ( x, y) = 0. We …
Web14 mrt. 2024 · proved a gen us formula for irreducible curves of the form f (x) = g (y) where f ( x ) and g ( x ) are nonconstant polynomials over an algebraically closed field of …
Web24 mrt. 2024 · There are a number of formulas variously known as Hurwitz's formula. The first is zeta(1-s,a)=(Gamma(s))/((2pi)^s)[e^(-piis/2)F(a,s)+e^(piis/2)F(-a,s)], where … dwayne foote kentuckyWebCorollary 221 (Riemann-Hurwitz formula). Let f : X ! Y be a finite morphism of curves of degree n. Then 2g(X)2=n·(2g(Y)2)+degR = n·(2g(Y)2)+ X P2X (e P 1). Example 222. By … crystal expansionWeb21 nov. 2006 · We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of … crystal exhibitionWebdata:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAB4CAYAAAB1ovlvAAAAAXNSR0IArs4c6QAAAw5JREFUeF7t181pWwEUhNFnF+MK1IjXrsJtWVu7HbsNa6VAICGb/EwYPCCOtrrci8774KG76 ... dwayne foote and darla jean stanton wikipediaWebTo use the Riemann-Hurwitz formula we need to compute $\deg (R) = \dim _ k \Gamma (R, \mathcal{O}_ R)$. By the structure of zero dimensional schemes over $k$ (see for … dwayne foote darla jean stantonWebHurwitz gave a simple formula when g= 0 (for any , [H]); his result was largely forgotten until recently. (Strehl has extended Hurwitz’s idea to a complete proof, [St].) Let l( ) be … dwaynefordWeb28 jan. 2024 · Classical Brill-Noether theory was born in the last century in order to describe the subchemes \(W^{k-1}_d\) of \({{\,\textrm{Pic}\,}}^d(C)\) parametrizing degree d-line bundles on a smooth curve C having at least k linearly independent global sections. Geometric properties of these loci (such as non-emptyness, irreducibily, connectedess, … crystal expensive