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arXiv · 2112.15130

Rational homogeneous spaces as geometric realizations of birational transformations

Gianluca Occhetta·Eleonora A. Romano·Luis E. Solá Conde·Jarosław A. Wiśniewski
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Abstract

A geometric realization of a birational map $\psi$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $\psi$ as the natural birational map among two extremal geometric quotients. In this paper we study geometric realizations of some classic birational maps --inversion maps, special Cremona transformations, special birational transformations of type $(2,1)$--, by considering $\mathbb{C}^*$-actions on certain rational homogeneous spaces and their subvarieties.

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Gianluca Occhetta, Eleonora A. Romano, Luis E. Solá Conde, Jarosław A. Wiśniewski. 2021-12-30. Rational homogeneous spaces as geometric realizations of birational transformations. https://doi.org/10.1007/s12215-023-00880-w

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