no code implementations • 27 Jul 2020 • Kathryn Heal, Avinash Kulkarni, Emre Can Sertöz
The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family.
1 code implementation • 24 Mar 2020 • Edgar Costa, Emre Can Sertöz
We give an algorithm that takes a smooth hypersurface over a number field and computes a $p$-adic approximation of the obstruction map on the Tate classes of a finite reduction.
Algebraic Geometry Number Theory 14C25, 14C22, 14F30, 14-04
no code implementations • 16 Aug 2019 • Marta Panizzut, Emre Can Sertöz, Bernd Sturmfels
We present a new normal form for cubic surfaces that is well suited for p-adic geometry, as it reveals the intrinsic del Pezzo combinatorics of the 27 trees in the tropicalization.
Algebraic Geometry 14Q10, 14J26, 14T05, 12J25
2 code implementations • 26 Nov 2018 • Pierre Lairez, Emre Can Sertöz
Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces.
Algebraic Geometry 32J25, 14Q10, 14C22, 32G20
2 code implementations • 21 Mar 2018 • Emre Can Sertöz
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension.
Algebraic Geometry Symbolic Computation 32G20, 14C30, 14D07, 14K20, 68W30
