In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the information necessary to reconstruct them. In particular, we consider some cases of actions of low complexity –measured in terms of two invariants of the action, called bandwidth and bordism rank– and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations.

Small bandwidth C*-actions and birational geometry / Occhetta, G.; Romano, E. A.; Solá Conde, E. L.; Wi?niewski, J. A.. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 2023, 32:(2023), pp. 1-57. [10.1090/jag/808]

Small bandwidth C*-actions and birational geometry

Occhetta, G.;Romano, E. A.;Solá Conde, E. L.
;
Wi?niewski, J. A.
2023-01-01

Abstract

In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the information necessary to reconstruct them. In particular, we consider some cases of actions of low complexity –measured in terms of two invariants of the action, called bandwidth and bordism rank– and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations.
2023
Occhetta, G.; Romano, E. A.; Solá Conde, E. L.; Wi?niewski, J. A.
Small bandwidth C*-actions and birational geometry / Occhetta, G.; Romano, E. A.; Solá Conde, E. L.; Wi?niewski, J. A.. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 2023, 32:(2023), pp. 1-57. [10.1090/jag/808]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/381729
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