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created: 2023-03-26T11:58
updated: 2023-04-11T23:20
aliases: ["Untitled"]
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- Tags: 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- #todo/create-links 

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# Personal review

- [ ] What is a Heegner divisor?
- [ ] What is the Hodge bundle?
- [ ] What is an elliptic pencil?
- [ ] Describe the Horikawa construction.
- [x] What is a bielliptic map? ✅ 2023-04-05
	- [ ] $\abs{D}$ bielliptic $\implies$ the restriction of $\phi_{\abs D}$ to a general member is a double cover of an elliptic curve. 
- [x] What is the Enriques lattice? ✅ 2023-04-05
	- [ ] $M\da U(2) \oplus E_8(-2) = \pi^*(H^2(\K3; \ZZ))$ for $\pi: \K3\to S$.
	- [ ] $H^2(S; \ZZ) = U \oplus E_8(-1) \times C_2$
	- [ ] One of these is $\rm{II}_{2, 10}$.
- [x] Describe a Type I degeneration. ✅ 2023-04-05
	- [ ] $X_0 =$ smooth irreducible variety.
- [x] Describe a Type II degeneration. ✅ 2023-04-05
	- [ ] $X_0 =$ chain with ends = rational surfaces and interior = have a minimal model ruled over an elliptic curve, intersections are elliptic curves
- [x] Describe a Type III degeneration. ✅ 2023-04-05
	- [ ] $X_0 =$ rational surfaces with $\Gamma(X_0) \isoas{\mathrm{PL}} S^2$.