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ALGEBRAIC SURFACES WITH INFINITELY MANY TWISTOR LINES

Published online by Cambridge University Press:  24 May 2019

A. ALTAVILLA*
Affiliation:
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131, Ancona, Italy email [email protected]
E. BALLICO
Affiliation:
Dipartimento Di Matematica, Università di Trento, Via Sommarive 14, 38123, Povo, Trento, Italy email [email protected]

Abstract

We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalisation map of a surface, we give constructive existence results for even degrees.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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Footnotes

Both authors are members of GNSAGA of INdAM; the first author was supported by SIR grants, Nos. RBSI14CFME and RBSI14DYEB, and an INdAM fellowship and thanks the Clifford Research Group at Ghent University where this fellowship was spent; the second author was supported by a grant from MIUR PRIN 2015.

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