Real multiplication on K3 surfaces and Kuga Satake varieties

By Bert van Geemen. 2006

52 citations recorded by the source corpus.

The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate various open problems related to the Hodge conjecture.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fd81b18feea8fc41e936f47feddbf818a8e6f2db

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. D. Huybrechts
2. Franccois Charles

In Geometry and Topology

1. Franccois Charles
2. D. Huybrechts
3. E. Markman
4. Max Lieblich
5. Kieran G. O’Grady
6. C. Liedtke
7. P. Stellari
8. Emanuele Macrì

In Mathematical Physics

1. D. Huybrechts
2. Franccois Charles
3. P. Stellari
4. Max Lieblich
5. Emanuele Macrì
6. E. Markman
7. C. Liedtke
8. Keiji Oguiso

Citations in the corpus

• Lectures on K3 Surfaces (2016, background): “such that the ring EndHdg(T (X)) is a totally real field, has been studied by van Geemen [202] and Schlickewei [525].”
• On the Picard number of K3 surfaces over number fields (2011, background): “There exist such K3 surfaces by [26], section 3, and they give new examples of K3 surfaces with infinitely many rational curves.”