7
votes
0answers
134 views

Global sections of vector bundles on a complex elliptic curve and analytic functions

Let me fix an elliptic curve $E$ over complex numbers with distinguished point $x \in E$. Thanks to Atiyah we know everything about discreet parameters of vector bundles and its moduli spaces. But I ...
1
vote
1answer
96 views

Theta function: Absolute convergence

I have to proof that the series $$ \theta (z)= \sum_{n=-\infty}^{+\infty} e^{\pi i [n^{2} \tau + 2nz]}$$ converges absolutely and uniformly on compact subsets of $\mathbb{C}$. Necessary and sufficient ...
2
votes
0answers
165 views

What is meant by a set of generic points on a compact Riemann surface

Let $X$ be a compact connected Riemann surface of genus $g \geq 1$. I'm studying a theorem of Faltings which looks as follows. Let $P_1,\ldots, P_g$ be generic points on $X$. Then we have some ...