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date: 2021-10-26 01:24
modification date: Tuesday 26th October 2021 23:55:05
title: translation surface
aliases: [translation surface]
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Last modified date: <%+ tp.file.last_modified_date() %>

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- Tags: 
	- #homotopy/bundles #AG 
- Refs:
	- #todo/add-references
- Links:
	- [Tilings VRG Index](Tilings%20VRG%20Index.md)
	- [translation surfaces](translation%20surfaces)


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# translation surface

- General theory of [moduli stack of elliptic curves](moduli%20stack%20of%20elliptic%20curves.md)
- How to compute genus of polygon-identification surface
- The [canonical bundle](canonical%20bundle.md) and its sections
- Holomorphic forms
- [Branched cover](Branched%20cover)
- [Riemann-Roch](Riemann-Roch.md)
- Homology of a bundle
- [divisor](divisor.md) 
- [Line bundles](Line%20bundles)
- For $V \to L \to X$ a line bundle, $\OO(L)$ is the sheaf of holomorphic - sections of $L$.
 -Structure Sheaf
- [Serre twist](Serre%20twist)
- [O of One](O%20of%20One)
- $\OO(1)$ is a [line bundle](line%20bundle.md)? 
	- And $\OO(k) = \OO(1)^{\tensor k}$?