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Apr
21
asked Index of a zero of a normal vector field
Apr
20
awarded  Nice Question
Apr
15
answered On the construction of hyperelliptic Riemann surfaces.
Mar
17
comment Line bundle of degree 1 on a genus 2 surface without global holomorphic sections
This is in Gunning, Lectures on Riemann Surfaces, chapter 7.b, in the discussion after Theorem 13.
Mar
17
comment Line bundle of degree 1 on a genus 2 surface without global holomorphic sections
related: math.stackexchange.com/q/1193907/22002
Mar
17
asked Line bundle of degree 1 on a genus 2 surface with 2 independent global holomorphic sections
Mar
9
asked Line bundle of degree 1 on a genus 2 surface without global holomorphic sections
Mar
9
answered Cocycle condition for line bundles.
Mar
2
accepted Divisor of meromorphic section of point bundle over a Riemann surface
Feb
22
accepted Length of geodesic representative on hyperbolic surfaces
Feb
22
comment Length of geodesic representative on hyperbolic surfaces
yes; could you explain how it can be used to answer my question?
Feb
21
comment Length of geodesic representative on hyperbolic surfaces
Thanks for this complete answer. There's a point I don't get. $\gamma_1 \delta$ is a path from $x$ to $y$, and $\alpha$ is the geodesic path which is path homotopic to $\gamma_1 \delta$, so I would expect it to be shorter than $\gamma_1 \delta$, i.e. $L(\alpha)\leq \dfrac{1}{2}L(\gamma)+L(\delta)$. But you wrote an inequality which is equivalent to $L(\delta)\leq \dfrac{1}{2}L(\gamma)+L(\alpha)$...how do you get it?
Feb
20
revised Hyperbolic (and related) structures on open unit disk
deleted 11 characters in body
Feb
20
comment Dehn twist as isometries on hyperbolic surface
I have edited my answer and tried to describe explicitly an example in genus 1. Hope it helps.
Feb
20
revised Dehn twist as isometries on hyperbolic surface
added 2003 characters in body
Feb
16
revised Length of geodesic representative on hyperbolic surfaces
added 11 characters in body
Feb
16
comment Length of geodesic representative on hyperbolic surfaces
lower bound; something like $l(\gamma) > f(l(\alpha),l(\beta))$ for some function; I have edited the question, thanks
Feb
16
asked Length of geodesic representative on hyperbolic surfaces
Feb
16
asked Maximal tori in Lie vs algebraic groups
Feb
16
comment Maximal tori in lie groups?
I think the statement is false, stated in this way. For instance in $\mathbb{C}^*$ a maximal torus (i.e. maximal compact connected abelian Lie subgroup) is given by $S^1$, which is not maximal abelian, since $\mathbb{C}^*$ itself is abelian. This of course generalizes to $GL(n,\mathbb{C})$ for higher $n$.