My research is in algebraic geometry and arithmetic geometry, with a focus on elliptic surfaces and fibrations.
My current project concerns torsion multisections of elliptic surfaces. I study the closure of torsion points in families of elliptic curves, particularly their behavior near singular fibers. My work combines local calculations involving monodromy and singular fibers with global questions about the irreducible components and genera of torsion multisections.
I am also interested in extending these questions to elliptic K3 surfaces and higher-dimensional abelian fibrations.
E. Sgallová, Torsion Points in Families of Elliptic Curves, 2026. arXiv:2611.08190.
V. Kala, E. Sgallová, and M. Tinková, Arithmetic of Cubic Number Fields: Jacobi–Perron, Pythagoras, and Indecomposables, Journal of Number Theory 273 (2025), 37–95.
J. Glivická, E. Sgallová, and J. Šaroch, Controlling Distribution of Prime Sequences in Discretely Ordered Principal Ideal Subrings of Q[x], Proceedings of the American Mathematical Society 151 (2023), no. 8, 3281–3290.
J. Krásenský, M. Raška, and E. Sgallová, Pythagoras Numbers of Orders in Biquadratic Fields, Expositiones Mathematicae 40 (2022), no. 4, 1181–1228.
E. Sgallová, Torsion Multisections on Elliptic Surfaces, in preparation.
F. Greer, C. Lian, and E. Sgallová, Shimura Lifts and Moduli of Abelian Surfaces, in preparation.