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2022-09-28
To look up:
- plurigenera
- irregularity. Irregular are easier, but lose the Albanese and you know less about the geometry.4
- Kodaira dimension. 1 and 2 are easy, 0 and \(-\infty\) are more difficult (for surfaces).
- Semiabelian varieties
- Quasiprojective varieties
- Universal property of the Albanese variety.
- Elliptic K3 surfaces, \(X\to {\mathbf{P}}^1\) fibers of type \(IV^*, F_1, F_2, F_3\).
- dominant morphisms
- finite morphism
- Log-ramification formula.
Misc
Complete curves and smooth complete surfaces are always projective:
A Picard group with torsion:
