We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Hodge similarities, algebraic classes, and Kuga–Satake varieties.
- Authors
Varesco, Mauro
- Abstract
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture for these Hodge morphisms. Studying K3 surfaces with a symplectic automorphism, we prove the Hodge conjecture for the square of the general member of the first four-dimensional families of K3 surfaces with totally real multiplication of degree two. We then show the functoriality of the Kuga–Satake construction with respect to Hodge similarities. This implies that, if the Kuga–Satake Hodge conjecture holds for two hyperkähler manifolds, then every Hodge similarity between their transcendental lattices is algebraic after composing it with the Lefschetz isomorphism. In particular, we deduce that Hodge similarities of transcendental lattices of hyperkähler manifolds of generalized Kummer deformation type are algebraic.
- Subjects
ISOMORPHISM (Mathematics); LOGICAL prediction; MORPHISMS (Mathematics); MULTIPLICATION
- Publication
Mathematische Zeitschrift, 2023, Vol 305, Issue 4, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-023-03390-8