74 citations · 304 across the 21 of their papers we have counts for
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A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line
Eric Pichon-Pharabod
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This…
Effective homology and periods of complex projective hypersurfaces
Pierre Lairez, Eric Pichon-Pharabod, Pierre Vanhove
We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of th…
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…
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…
The boundary of the orbit of the 3 by 3 determinant polynomial
Jesko Hüttenhain, Pierre Lairez
We consider the 3 by 3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables.…
Computing the Chow variety of quadratic space curves
Peter Bürgisser, Kathlén Kohn, Pierre Lairez +1
Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces. Following Gel'fand, Kapranov and Zele…
Resolution except for minimal singularities II. The case of four variables
Edward Bierstone, Pierre Lairez, Pierre D. Milman
In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singul…