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ag.algebraic geometry – References for equivariant Okay-theory Answer

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ag.algebraic geometry – References for equivariant Okay-theory

I’ve spent the final few days1 Reading references to the equivariate Okay-theory. I’ve simply compiled the next bibliography for my collaborators and behold no intuition to not publish it. This checklist leans closely in the direction of combinatorics and classical algebraic geometry.

My common conclusion is that there are a number of good references to equivariate Okay-theory localization, however they’re all too dense for somebody who has by no means seen these items earlier than. Fortunately, there are good, dilatory introductions to equivariant cohomology, and the 2 areas are comparable sufficient you could get the motivation and examples from the cohomology papers after which dive into the Okay-theory volumes.

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Short papers with many exquisite examples

1: Julianna Tymoczkos introduction to equivariant cohomology, An introduction to the equivariant cohomology and homology in response to Goresky, Kottwitz and MacPherson

2: Early elements of Knutson Tao’s paper Riddle and (equivariant) cohomology of the Grassmannians, on the equivariant cohomology of Grassmann’s

More circumstantial references to equivariate cohomology:

3: Fultons Remarks (since changed by the bespeak Equivariate cohomology in algebraic geometry). For localization behold Lecture 4 and 5, Lecture 6 – 10 on the peculiarities of homogeneous rooms.

4: Section 2 of Guillemin and Zara’s first paper, Equivariate de Rham principle and graph, explains which elements of the story are absolute combinatorics.

References particularly for the Okay-theory

5: Chapters 5 and 6 of Complex geometry and illustration principle, by Chriss and Ginzburg. Lots and plenty of particulars, and significantly focuses on flag variants. One of the few locations I’ve create that describes tips on how to get to something apart from some extent.

6: Guillemin’s and Zara’s Okay-theory paper G-actions on graphics. This is just like their earlier paper that I’m quoting, however shorter and for the Okay-theory.

7: A paper from Nielsen, Diagonal linearized coherent sliceswhich appears to have anticipated many outcomes on this region and consists of some exquisite examples on the aim. (Note that MathSciNet evaluate the hyperlink is in french, however the paper is in English.)

8: Knutson and Rosus paper Equivariant Okay-Theory and Equivariant Cohomology, Establish localization within the equivariate Okay-theory and elucidate equivariate Grothendieck-Riemann-Roch.

William Fulton too tells me that he and Graham are engaged on an explanatory article that I anticipate will breathe excellent.

1 For the inquisitive, this isn’t my first time erudition this materials. Rather, I initially erudite by scanning a whole lot of papers, going to lectures, and asking Allen Knutson about something that confused me. I’m now enjoying the position of All for others, so I necessity to be taught the matter higher.

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