Complex Multiplication in Twistor Spaces

Daniel Huybrechts

Type: Article

Publication Date: 2020-03-17

Citations: 2

DOI: https://doi.org/10.1093/imrn/rnaa073

Abstract

Abstract Despite the transcendental nature of the twistor construction, the algebraic fibres of the twistor space of a K3 surface share certain arithmetic properties. We prove that for a polarised K3 surface with complex multiplication, all algebraic fibres of its twistor space away from the equator have complex multiplication as well.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (16)

Action	Title	Year	Authors
+	Moduli of K3 Surfaces and Abelian Varieties	2005	Jordan Rizov
+ PDF Chat	Scalar Curvature and Projective Embeddings, I	2001	Simon Donaldson
+ PDF Chat	Hyperkähler metrics and supersymmetry	1987	Nigel Hitchin A. Karlhede Ulf Lindström M. Roček
+	Kähler-Einstein metrics and projective embeddings	2000	Dominique Hulin
+ PDF Chat	Real multiplication on K3 surfaces and Kuga Satake varieties	2008	Bert van Geemen
+	On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I	1978	Shing‐Tung Yau
+	K3 surfaces with algebraic period ratios have complex multiplication	2015	Paula Tretkoff
+	Calabi-Yau Manifolds and Related Geometries	2003	Mark Gross Dominic Joyce Daniel Huybrechts
+	Lectures on K3 Surfaces	2016	Daniel Huybrechts
+	Every rational Hodge isometry between two K⁢3K3 surfaces is algebraic	2017	Nikolay Buskin