---
created: 2023-04-17T12:22
updated: 2023-04-17T12:22
---


---
date: 2022-07-07 13:14
modification date: Thursday 7th July 2022 13:14:25
title: "2022-07-07"
aliases: [2022-07-07]
---

Last modified date: NaN

---

- Tags: 
	- #web/quick-notes #research/notes
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

---

# 2022-07-07

[Current reading: Voison on the Luroth problem](https://webusers.imj-prg.fr/~claire.voisin/Articlesweb/jdgvoisin.pdf) 

- [ ] What does it mean for a variety to be unirational?
- [ ] What is a dominant rational map?
- [ ] What is a blowup along a smooth center?
- [ ] When does unirationality imply rationality?
- [ ] What methods were used to determine solutions to the Luroth problem in dimensions $d\geq 3$?
- [ ] What is a *very general* hypersurface?
- [ ] Give examples of cubic hypersurfaces.
- [ ] State a form of GAGA.
- [ ] What is a rationally connected variety?
- [ ] What is the Brauer group?
- [ ] What is the Artin-Mumford invariant?
- [ ] Describe $\OO_{\PP^n}(m)$ in equations.
- [ ] What is [Abel theorem](Unsorted/Abel-Jacobi%20map.md)?
- [ ] What is Bloch's famouse conjecture?
	- [ ] $H^0(X; \Omega_{X\slice k}^{\geq 1}) = 1 \implies \CH_0(X) = 1$ 
- [ ] What is map identifying $\CH^1(X) \iso \Pic(X)$?
- [ ] Describe the Hodge decomposition and the Hodge diamond.
- [ ] What is an integral Hodge class?
- [ ] What is the Lefschetz (1, 1) theorem?
- [ ] What is the cycle class map? What is its image?
- [ ] What is unramified cohomology?
- [ ] What is the intermediate Jacobian?
- [ ] What is the Lefschetz decomposition on homology?
- [ ] What is the Abel-Jacobi map?
- [ ] What is the $\del\delbar$ lemma?
- [ ] What is the theta divisor?
- [ ] What is a unimodular intersection pairing?