C*-actions on rational homogeneous varieties and the associated birational maps

Given a birational map among projective varieties, it is known that there exists a variety Z with a one-dimensional torus action such that the birational map is induced from two geometric quotients of Z. We proceed in the opposite direction: given a smooth projective variety X with a one-dimensional torus action, one can define a birational map associated to the action and study the properties of the map via the geometry of X. Rational homogeneous varieties admit natural torus actions, so they are a good class of example to test the general theory. In the thesis, we obtain and discuss some results about the birational maps associated to some one-dimensional torus actions on rational homogeneous varieties.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2023

Author dc:creator

• Franceschini, Alberto

Contributors dc:contributor

• Sola Conde, Eduardo Luis

• torus actions, rational homogeneous varieties, birational geometry
• Settore MAT/03 - Geometria

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Tutti i diritti riservati (All rights reserved)
• license uri:iris.PRI01

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_372282
10.15168/11572_372282

OAI identifier oai:identifier

oai:iris.unitn.it:11572/372282