Timeline for Quasi-unipotent monodromy for general families
Current License: CC BY-SA 3.0
6 events
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| Jul 23, 2012 at 3:07 | comment | added | Tony Pantev | Two classical references are the paper "Periods of integrals on algebraic manifolds III", Publ. Math. IHES 38 (1970) by Griffiths and the paper "Variation of Hodge structure: the singularities of the period mapping" Invent. math. 22 (1973) by Schmid. They in particular explain Borel's proof of the quasi-unipotency theorem that I mentioned above. There are many other modern references. For instance, you may want to take a look at the excellent book "Period mappings and period domains" by Carlson, Mueller-Stach, and Peters. | |
| Jul 23, 2012 at 3:00 | comment | added | Tony Pantev | Ah, I noticed I missed an adjective in the comment - I was defining what it means for $G$ to be quasi-unipotent. I edited the answer to reflect this correctly. The unipotency of $mon$ is defined in a similar manner - we say that $mon$ is unpotent, when $G$ is a connected unipotent algebraic group, i.e. when when it coincides with its unipotent radical. The references are numerous and the applications are usually Hodge theoretic. The quasi-unipotency of a local systen can is also very useful when we compute cohomology. | |
| Jul 23, 2012 at 2:36 | history | edited | Tony Pantev | CC BY-SA 3.0 |
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| Jul 22, 2012 at 10:01 | vote | accept | Jack | ||
| Jul 22, 2012 at 6:46 | comment | added | Jack | Thank you very much for your beautiful answer. I had never known of this general definition of quasi-unipotency. I have some more questions: First of all what is the best reference which discusses this definition and it's consequences. Secondly, if this is the definition of "quasi-unipotency", then what would be the definition of "unipotency" in general? | |
| Jul 22, 2012 at 0:47 | history | answered | Tony Pantev | CC BY-SA 3.0 |