Graphs of schemes associated to group actions

Date

2023-12-01

Author

Kişisel, Ali Ulaş Özgür
Özkan, Engin

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Let X be a proper algebraic scheme over an algebraically closed field. We assume that atorus T acts on X such that the action has isolated fixed points. The T-graph of X canbe defined using the fixed points and the one-dimensional orbits of the T-action. If theupper Borel subgroup of the general linear group with maximal torus T acts on X, thenwe can define a second graph associated to X, called the A-graph of X. We prove thatthe A-graph of X is connected if and only if X is connected. We use this result to giveproof of Hartshorne’s theorem on the connectedness of the Hilbert scheme in the case ofd points in n-dimensional projective space.

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https://dergipark.org.tr/en/download/article-file/2779510
https://hdl.handle.net/11511/104966

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Department of Mathematics, Article