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.
| Identifer | oai:union.ndltd.org:unitn.it/oai:iris.unitn.it:11572/372282 |
| Date | 20 March 2023 |
| Creators | Franceschini, Alberto |
| Contributors | Franceschini, Alberto, Sola Conde, Eduardo Luis |
| Publisher | Università degli studi di Trento, place:TRENTO |
| Source Sets | Università di Trento |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/doctoralThesis |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | firstpage:1, lastpage:124, numberofpages:124 |
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