Details
| Original language | English |
|---|---|
| Pages (from-to) | 309-324 |
| Number of pages | 16 |
| Journal | Manuscripta mathematica |
| Volume | 168 |
| Issue number | 3-4 |
| Early online date | 25 May 2021 |
| Publication status | Published - Jul 2022 |
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.
Keywords
- Hodge theory, Hyperkähler varieties, Motives, Mumford–Tate conjecture
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Manuscripta mathematica, Vol. 168, No. 3-4, 07.2022, p. 309-324.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Mumford–Tate conjecture for hyperkähler varieties
AU - Floccari, Salvatore
N1 - Funding Information: I am most grateful to Ben Moonen and Arne Smeets for their careful reading and the many comments, which substantially improved this text. I am also thankful to the anonymous referee for his/her, comments.
PY - 2022/7
Y1 - 2022/7
N2 - 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.
AB - 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.
KW - Hodge theory
KW - Hyperkähler varieties
KW - Motives
KW - Mumford–Tate conjecture
UR - http://www.scopus.com/inward/record.url?scp=85106459041&partnerID=8YFLogxK
U2 - 10.1007/s00229-021-01316-4
DO - 10.1007/s00229-021-01316-4
M3 - Article
AN - SCOPUS:85106459041
VL - 168
SP - 309
EP - 324
JO - Manuscripta mathematica
JF - Manuscripta mathematica
SN - 0025-2611
IS - 3-4
ER -