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created: 2023-04-17T12:22
updated: 2024-01-01T23:13
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date: 2022-09-28 15:27
modification date: Wednesday 28th September 2022 15:27:58
title: "2022-09-28"
aliases: [2022-09-28]
---

Last modified date: NaN

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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# 2022-09-28


To look up:

- [ ] [plurigenera](Unsorted/birational%20geometry.md)
- [ ] [irregularity](Unsorted/birational%20geometry.md). Irregular are easier, but lose the Albanese and you know less about the geometry.4
- [ ] [Kodaira dimension](Unsorted/Enriques-Kodaira%20Classification.md). 1 and 2 are easy, 0 and $-\infty$ are more difficult (for surfaces).
- [ ] Semiabelian varieties
- [ ] Quasiprojective varieties
- [ ] Universal property of the [Albanese](Albanese) variety.
- [ ] Elliptic [K3 surfaces](K3%20surfaces.md), $X\to \PP^1$ fibers of type $IV^*, F_1, F_2, F_3$.
- [ ] [dominant](Unsorted/dominant%20morphism.md) morphisms
- [ ] [finite morphism](finite%20morphism)
- [ ] Log-ramification formula.

# Misc

Complete curves and smooth complete surfaces are always projective:

![](attachments/Pasted%20image%2020220928221007.png)

A Picard group with torsion:

![](attachments/Pasted%20image%2020220928231601.png)