On the Mumford-Tate conjecture for hyperkähler varieties
Abstract
We study the Mumford--Tate conjecture for hyperkähler varieties. We show that the full conjecture holds for all varieties deformation equivalent to either an Hilbert scheme of points on a K3 surface or to O'Grady's ten dimensional example, and all of their self-products. For an arbitrary hyperkähler variety whose second Betti number is not 3, we prove the Mumford--Tate conjecture in every codimension under the assumption that the Künneth components in even degree of its André motive are abelian. Our results extend a theorem of André.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.06238
- arXiv:
- arXiv:1904.06238
- Bibcode:
- 2019arXiv190406238F
- Keywords:
-
- Mathematics - Algebraic Geometry;
- 14C30;
- 14F20;
- 14J20;
- 14J32;
- 53C26
- E-Print:
- final version, to appear in Manuscripta Mathematica