---
date: 2022-05-25 20:03
modification date: Wednesday 25th May 2022 20:03:40
title: "2022-05-25"
aliases: [2022-05-25]
created: 2023-04-12T16:26
updated: 2023-04-17T12:22
---

Last modified date: NaN

---

- Tags: 
	- #research/dynkin-project #web/quick-notes #research/notes
- Refs:
	- #todo
- Links:
	- [< 2022-05-20](2022-05-20.md)
	- [> 2022-05-25](2022-05-25.md)



---

# 05-25-2022


Definitions:

- Basics
	- [ ] [normalization](Unsorted/normalization.md)
	- [ ] [toric variety](Unsorted/toric.md)
	- [ ] [weighted projective space](Unsorted/weighted%20projective%20space.md)
	- [ ] [Cartier divisor](Unsorted/Weil%20divisor.md)
	- [ ] [blowup](Unsorted/blowup.md) and [blowdown](blowdown)
	- [ ] [contraction (of curves)](Unsorted/contraction%20(of%20curves).md)
	- [ ] [ample](Unsorted/ample.md)
	- [ ] [flat family](Unsorted/flat%20family.md)
	- [ ] [discriminants](Unsorted/discriminants.md)
	- [ ] [[pencil]]
- Lie theory
	- [ ] [[fundamental character]]
	- [ ] [character lattice](character%20lattice)
	- [ ] There is an isomorphism $\CC\adjoin{\Lambda\dual}^{W_\lambda} \cong \CC\adjoin{\chi_1, \cdots, \chi)n}$ where $\chi_i = \chi(\bar\omega_i)$ are the characters of the [[fundamental weights]]. 
	  - [ ] This yields $T_{\Lambda\dual}/W_{\lambda} \cong \AA^n$ with coordinates $\chi_i$.
	- [ ] [dominant weight](dominant%20weight)
	- [ ] [[Coxeter fan]]
	- [ ] [[simple root]]
	- [ ] [[Weyl character formula]]
	- [ ] [[root lattice]]
	- [ ] [[weight lattice]]
	- [ ] [[discriminant locus]]
- Moduli of pairs:
	- [ ] [stable curve](Unsorted/stable%20curve.md)
	- [ ] [semistable](Unsorted/semistable.md)
	- [ ] [[slc]]
	- [ ] [[stable pair]]
	- [ ] [del Pezzo surface](Unsorted/del%20Pezzo.md)
	- [ ] [[stable del Pezzo pair]]
- Moduli stacks
	- [ ] [DM stack](Unsorted/Deligne-Mumford%20stack.md)
	- [ ] [separated scheme](Unsorted/separated.md)
	- [ ] [algebraic space](Unsorted/algebraic%20space.md)
	- [ ] [finite type](Unsorted/finite%20type.md)