arXiv subjects

Flora Poon

Publications and source records attributed to Flora Poon.

3 recordsLinked to original sources

arXiv2025

Kuga-Satake construction on families of K3 surfaces of Picard rank 14

The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga-Satake construction. Furthermore, we illustrate how the the modular mapping can be realised for any specific families of K3 surfaces of Picard rank $14$, which can be specialised to families of K3 surfaces of higher Picard rank.

math.AG↗

arXiv2022

On two-elementary K3 surfaces with finite automorphism group

We study complex algebraic K3 surfaces of Picard ranks 11,12, and 13 of finite automorphism group that admit a Jacobian elliptic fibration with a section of order two. We prove that the K3 surfaces admit a birational model isomorphic to a projective quartic hypersurface and construct geometrically the frames of all supported Jacobian elliptic fibrations. We determine the dual graphs of all smooth rational curves for these K3 surfaces, the polarizing divisors, and the embedding of the reducible fibers in each frame into the corresponding dual graph.

math.AG↗

arXiv2021

Slopes of Siegel cusp forms and geometry of compactified Kuga varieties

We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in most cases it has canonical singularities. We then use results about the slope of Siegel modular forms to determine the Kodaira dimension for all g>1 and n>0.

math.AG↗