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2022-07-07
Current reading: Voison on the Luroth problem
- 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 \({\mathcal{O}}_{{\mathbb{P}}^n}(m)\) in equations.
- What is Abel theorem?
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What is Bloch’s famouse conjecture?
- \(H^0(X; \Omega_{X_{/ {k}} }^{\geq 1}) = 1 \implies {\operatorname{CH}}_0(X) = 1\)
- What is map identifying \({\operatorname{CH}}^1(X) { \, \xrightarrow{\sim}\, }{\operatorname{Pic}}(X)\)?
- 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 \({\partial}{ \mkern 1.5mu\overline{\mkern-1.5mu{\partial}\mkern-1.5mu}\mkern 1.5mu}\) lemma?
- What is the theta divisor?
- What is a unimodular intersection pairing?