17 citations · 63 across the 12 of their papers we have counts for
12 papers · 1 filter
Computing transcendence and linear relations of 1-periods
Emre Can Sertöz, Joël Ouaknine, James Worrell
A 1-period is a complex number given by the integral of a univariate algebraic function, where all data involved -- the integrand and the domain of integration -- are defined over…
Computing heights via limits of Hodge structures
Spencer Bloch, Robin de Jong, Emre Can Sertöz
We consider the problem of explicitly computing Beilinson--Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a…
Heights on curves and limits of Hodge structures
Spencer Bloch, Robin de Jong, Emre Can Sertöz
We exhibit a precise connection between Néron--Tate heights on smooth curves and biextension heights of limit mixed Hodge structures associated to smoothing deformations of singula…
Separation of periods of quartic surfaces
Pierre Lairez, Emre Can Sertöz
We give a computable lower bound on the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determinatio…
Effective obstruction to lifting Tate classes from positive characteristic
Edgar Costa, Emre Can Sertöz
We give an algorithm that takes a smooth hypersurface over a number field and computes a -adic approximation of the obstruction map on the Tate classes of a finite reduction. Th…
On reconstructing subvarieties from their periods
Hossein Movasati, Emre Can Sertöz
We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X.…
A numerical transcendental method in algebraic geometry
Pierre Lairez, Emre Can Sertöz
Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces. We also study the lattice reduction technique that…
Prym varieties of genus four curves
Nils Bruin, Emre Can Sertöz
Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic…
Certifying reality of projections
Jonathan Hauenstein, Avinash Kulkarni, Emre Can Sertöz +1
Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., s…
Computing Periods of Hypersurfaces
Emre Can Sertöz
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the period…
Computing images of polynomial maps
Corey Harris, Mateusz Michałek, Emre Can Sertöz
The image of a polynomial map is a constructible set. While computing its closure is standard in computer algebra systems, a procedure for computing the constructible set itself is…
A compactification of the moduli space of multiple-spin curves
Emre Can Sertöz
We construct a smooth Deligne-Mumford compactification for the moduli space of curves with an m-tuple of spin structures using line bundles on quasi-stable curves as limiting objec…