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Here is a small collection of pictures and animations starring varieties which are of interest in resolution of singularities in algebraic geometry and number theory.

The goal of the project is to develop theories and algorithms for solving problems related to the resolution of singularities in algebraic geometry and number theory. The three main subareas of research are the following.

RES

Computing resolutions for various classes of varieties: The main punching line will be dimension two and three, both in characteristic zero and p. The reason is two-fold. First, we think that effective resolutions of 4-folds is practically too costly in terms of computing resources (although theoretically possible). Second, many interesting applications and phenomena happen to appear already in dimension two and three.

ALG

Solving problems in algebraic geometry related to resolution: This concerns the canonical class of an algebraic variety, in particular the parametrization problem for rational surfaces, the problem of finding rational and elliptic fibrations, and the problem of constructing canonical embeddings.

NUM

Solving problems in number theory related to resolution: The problems are related to p-adic completions and global fields, such as the computation of normal bases in number fields, or the existence problem of rational points on Del Pezzo surfaces.