New York Journal of Mathematics
Volume 29 (2023), 1117-1148


Amedeo Altavilla, Edoardo Ballico, and Maria Chiara Brambilla

Twistor fibers in hypersurfaces of the flag threefold

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Published: October 27, 2023.
Keywords: Flag threefold, twistor projection, twistor fiber, surfaces, bidegree.
Subject [2010]: Primary: 32L25, 14M15; Secondary: 14D21, 32M10, 14J26.

We study surfaces of bidegree (1,d) contained in the flag threefold in relation to the twistor projection. In particular, we focus on the number and the arrangement of twistor fibers contained in such surfaces. First, we prove that there is no irreducible surface of bidegree (1,d) containing d+2 twistor fibers in general position. On the other hand, given any collection of (d+1) twistor fibers satisfying a mild natural constraint, we prove the existence of a surface of bidegree (1,d) that contains them. We improve our results for d=2 or d=3, by removing all the generality hypotheses.


All the authors are partially supported by GNSAGA. The first named author is partially supported by the INdAM project `Teoria delle funzioni ipercomplesse e applicazioni'.

Author information

Amedeo Altavilla
Dipartimento di Matematica
Universita degli Studi di Bari `Aldo Moro'
Via Edoardo Orabona, 4, 70125, Bari, Italia


Edoardo Ballico
Dipartimento Di Matematica
Universita di Trento
Via Sommarive 14, 38123, Povo, Trento, Italia


Maria Chiara Brambilla
Universita Politecnica delle Marche
Via Brecce Bianche, I-60131 Ancona, Italia