Year: 2025
Type: article
Abstract: For each $$k \ge 5$$ k ≥ 5 we give a counterexample to a conjecture of Movasati on the dimension of certain Hodge loci of cubic hypersurfaces in $$\textbf{P}^{2k+1}$$ P 2 k + 1 containing two k -planes intersecting in dimension $$k-3$$ k - 3 . We give similar examples for Hodge loci of cubic hypersurfaces in $$\textbf{P}^{2k+1}$$ P 2 k + 1 containing two k -planes intersecting in dimension $$k-2$$ k - 2 and for quartic hypersurfaces in $$\textbf{P}^{2k+1}$$ P 2 k + 1 containing two k -planes intersecting in dimension $$k-2$$ k - 2 . Moreover, we present new evidence for Movasati’s conjecture for the values of k for which our type of counterexamples cannot exist, i.e., for $$k=3,4$$ k = 3 , 4 .
Author: Remke Kloosterman
Institution: University of Padua
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4413356018