2022-08-10

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2022-08-10

attachments/Pasted%20image%2020220810104956.png

attachments/Pasted%20image%2020220810105105.png attachments/Pasted%20image%2020220810105125.png

A nicer proof of smoothness:

attachments/Pasted%20image%2020220810105226.png

Simplicial vs smooth attachments/Pasted%20image%2020220810105331.png

Some interesting references on creating stacky fans from Cartan matrices: http://www.mi.uni-koeln.de/DFG-Schwerpunkt/VortraegeThurnau/MarkBlume.pdf#page=21&zoom=auto,-91,249 attachments/Pasted%20image%2020220810113726.png

Completeness and properness: attachments/Pasted%20image%2020220810114624.png

Distinguished points: attachments/Pasted%20image%2020220810114924.png

Orbits in terms of quotient lattices: attachments/Pasted%20image%2020220810115133.png

Orbit-cone correspondence: attachments/Pasted%20image%2020220810115222.png

attachments/Pasted%20image%2020220810115359.png

Star fans: attachments/Pasted%20image%2020220810115452.png attachments/Pasted%20image%2020220810115541.png attachments/Pasted%20image%2020220810115607.png

Introducing a ray into a cone to subdivide modifies \(X_\Sigma\) at the distinguished point of \(U_\sigma\).

Stellar refinements: attachments/Pasted%20image%2020220810115913.png

Singular and smooth loci: attachments/Pasted%20image%2020220810120105.png attachments/Pasted%20image%2020220810120148.png

Divisors

attachments/Pasted%20image%2020220810120921.png

Restriction: attachments/Pasted%20image%2020220810121055.png

attachments/Pasted%20image%2020220810121113.png

attachments/Pasted%20image%2020220810121640.png attachments/Pasted%20image%2020220810121651.png

example computations of divisor class groups

attachments/Pasted%20image%2020220810122920.png

Characterizing when Weil = Cartier: attachments/Pasted%20image%2020220810123117.png

Intersection products

attachments/Pasted%20image%2020220810123558.png

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