Abstract:
I will discuss an algorithm to decide the finite generation of a (multi) graded ring. For $N$-gradings, it is the analog of Erathostenes' sieve method. For $N^2$-gradings, it is the algebraic analog of the Kahler-Ricci flow.
The division flow breaks up a finitely generated graded ring into its simplest blocks, a so called linearity fan. I will discuss the properties of the linearity fan. One application is to characterize the chambers and walls in the Log Geography introduced by Shokurov.
Language: English
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