Graphs of schemes associated to group actions

Ali Özgür Kişisel; Engin Özkan

Article Details

Graphs of schemes associated to group actions

Authors:

Ali Özgür Kişisel | Engin Özkan

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.145-154

Document Type:

Article

Publication Date:

2/2024

Document Language:

English

Document ID (Org No.):

2001312254

pISSN:

2651-477X

Keywords:

Abstract:

 Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T-graph of X can be defined using the fixed points and the one-dimensional orbits of the T-action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A-graph of X. We prove that the A-graph of X is connected if and only if X is connected. We use this result to give proof of Hartshornes theorem on the connectedness of the Hilbert scheme in the case of d points in mathbbPn. .

 Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T-graph of X can be defined using the fixed points and the one-dimensional orbits of the T-action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A-graph of X. We prove that the A-graph of X is connected if and only if X is connected. We use this result to give proof of Hartshornes theorem on the connectedness of the Hilbert scheme in the case of d points in mathbbPn. .

 Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T-graph of X can be defined using the fixed points and the one-dimensional orbits of the T-action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A-graph of X. We prove that the A-graph of X is connected if and only if X is connected. We use this result to give proof of Hartshornes theorem on the connectedness of the Hilbert scheme in the case of d points in mathbbPn. .

 Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T-graph of X can be defined using the fixed points and the one-dimensional orbits of the T-action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A-graph of X. We prove that the A-graph of X is connected if and only if X is connected. We use this result to give proof of Hartshornes theorem on the connectedness of the Hilbert scheme in the case of d points in mathbbPn. .

Article Details

Graphs of schemes associated to group actions

Authors:

Ali Özgür Kişisel | Engin Özkan

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.145-154

Document Type:

Article

Publication Date:

2/2024

Document Language:

English

Document ID (Org No.):

2001312254

pISSN:

2651-477X

Hilbert scheme

Borel group action

A-graphHilbert scheme

Borel group action

A-grap

Issues

Article Details

Graphs of schemes associated to group actions

Authors: Ali Özgür Kişisel | Engin Özkan

Publisher: Hacettepe University

Main Topics: Mathematical Sciences

Journal: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.145-154

Document Type: Article

Publication Date: 2/2024

Document Language: English

Document ID (Org No.): 2001312254

pISSN: 2651-477X

Hilbert scheme

Borel group action

A-graphHilbert scheme

Borel group action

A-grap

Issues

Authors:

Ali Özgür Kişisel | Engin Özkan

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.145-154

Document Type:

Article

Publication Date:

2/2024

Document Language:

English

Document ID (Org No.):

2001312254

pISSN:

2651-477X