Timeline for Do divisors of degree g with this property exist in general

8 events

when toggle format	what		by	license	comment
Jan 14, 2022 at 20:08	vote	accept	Ariyan Javanpeykar
Dec 14, 2011 at 22:42	comment	added	François Brunault		It is not true that the answer is always yes for modular curves : for example, there could be only one cusp. In this direction Matthew Baker has proved that if $N>479$ is prime then there is no torsion packet at all on the modular curve $X_0^+(N) = X_0(N)/W_N$ (see his article Torsion points on modular curves).
Dec 14, 2011 at 21:29	history	edited	Ariyan Javanpeykar	CC BY-SA 3.0	added 61 characters in body
Dec 14, 2011 at 18:18	comment	added	Ariyan Javanpeykar		You're right. I wanted to exclude this example. And yes, I want $\mathcal{O}_X(D_i-D_j)$ to be a torsion element in the Picard group for all $i,j=1,\ldots,g$. Moreover, the $D_i$ are points (with multiplicity 1).
Dec 14, 2011 at 18:08	answer	added	Felipe Voloch		timeline score: 4
Dec 14, 2011 at 17:38	comment	added	Jack Huizenga		What is to stop $D = gP$ for some point $P\in X$? Also, is $\mathcal O_X(D_i-D_j)$ supposed to be torsion for every $i,j$?
Dec 14, 2011 at 17:26	history	edited	Ariyan Javanpeykar	CC BY-SA 3.0	added 5 characters in body
Dec 14, 2011 at 17:15	history	asked	Ariyan Javanpeykar	CC BY-SA 3.0