# Slice-polynomial functions and twistor geometry of ruled surfaces in $$\mathbb {CP}^3$$CP3

@article{Altavilla2017SlicepolynomialFA, title={Slice-polynomial functions and twistor geometry of ruled surfaces in \$\$\mathbb \{CP\}^3\$\$CP3}, author={Amedeo Altavilla and Giulia Sarfatti}, journal={Mathematische Zeitschrift}, year={2017}, volume={291}, pages={1059-1092} }

In the present paper we introduce the class of slice-polynomial functions: slice regular functions defined over the quaternions, outside the real axis, whose restriction to any complex half-plane is a polynomial. These functions naturally emerge in the twistor interpretation of slice regularity introduced in Gentili et al. (J Eur Math Soc 16(11):2323–2353, 2014) and developed in Altavilla (J Geom Phys 123:184–208, 2018). To any slice-polynomial function P we associate its companion$$P^\vee $$P…

## 11 Citations

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The purpose of this paper is to present several new, sometimes surprising, results concerning a class of hyperholomorphic functions over quaternions, the so-called slice regular functions. The…

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AbstractWe exploit techniques from classical (real and complex) algebraic geometry for the study of the standard twistor fibration $${\pi :
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This paper applies the results obtained in [3] to establish some outcomes of the study of the behaviour of a class of linear operators, which include the Sylvester ones, acting on slice semi-regular functions, and gives an Embry-type result which classifies the functions f and g such that for any function h commuting with f + g and f * g, the authors have that h commutes with f andG.

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Abstract The aim of this paper is to carry out an analysis of five trascendental operators acting on the space of slice regular functions, namely *-exponential, *-sine and *-cosine and their…

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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…

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In this paper, we shall investigate some generalized Bohr radius in the non-commutative setting of quaternions. To be precise, two results of Enrico Bombieri are generalized by means of a new idea…

### Slice Fueter-Regular Functions

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Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra O\documentclass[12pt]{minimal}…

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