Personal tools
You are here: Home Publications Multiplicative sub-Hodge structures of conjugate varieties

Multiplicative sub-Hodge structures of conjugate varieties

Stefan Schreieder

Number 25
Author Stefan Schreieder
Year 2013

For any subfield K of the complex numbers which is not contained in an imaginary quadratic number field, we construct conjugate varieties whose algebras of K-rational (p,p)-classes are not isomorphic. This compares to the Hodge conjecture which predicts isomorphisms when K is contained in an imaginary quadratic number field; additionally, it shows that the complex Hodge structure on the complex cohomology algebra is not invariant under the Aut(\C)-action on varieties. In our proofs, we find simply connected conjugate varieties whose multilinear intersection forms on their second real cohomology groups are not (weakly) isomorphic. Using these, we detect non-homeomorphic conjugate varieties for any fundamental group and in any birational equivalence class of dimension at least 10.

More information about this publication…

Document Actions
« February 2024 »
February
MoTuWeThFrSaSu
1234
567891011
12131415161718
19202122232425
26272829