---
- CiteKey: BHPV04
- Type: book
- Title: Compact complex surfaces,
- Author: Barth, Wolf P.; Hulek, Klaus; Peters, Chris A. M.; Ven, Antonius;
- Publisher: Springer Berlin Heidelberg,
- Year: 2004
---

# Compact complex surfaces

## Meta

- **URL**: <https://doi.org/10.1007/978-3-642-57739-0>
- **URI**: <http://zotero.org/users/1049732/items/HTKHVUZU>
- **Local File**: [Barth et al. - 2004 - Compact complex surfaces.pdf](file:///home/zack/Downloads/Zotero_Source/Springer%20Berlin%20Heidelberg/2004/Barth%20et%20al.%20-%202004%20-%20Compact%20complex%20surfaces.pdf)
- **Open in Zotero**: [Zotero](zotero://select/library/items/HTKHVUZU)

# Questions

- [ ] What is the length of a sheaf?
- [ ] What is a rational singularity?
- [ ] What is Artin's criterion?
- [x] What is a minimal surface? ✅ 2024-03-31
	- [ ] Contains no $(-1)\dash$curves.
	- [ ] Equivalently, $X$ is minimal if any birational morphism $X\to Y$ with $Y$ smooth is an isomorphism.
- [x] How do contractions affect betti numbers? ✅ 2024-03-31
	- [ ] Blowing down a $(-1)\dash$curve decreases $\beta_2$ by one.
- [x] How can one promote a birational map $f:X\to Y$ to a morphism? An isomorphism? ✅ 2024-03-31
	- [ ] Morphism if $K_Y$ is nef
	- [ ] Isomorphism if additionally $K_X$ is nef.
- [ ] 
## Abstract


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## Extracted Annotations