Arc Schemes And Singularities

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.

Acest titlu introduce teoria schemelor de arc in geometria algebrica si teoria singularitatii, cu accent special pe evolutiile recente din jurul problemei Nash pentru suprafete. Principalele provocari constau in a intelege structura globala si locala a schemelor de arc si modul in care acestea se raporteaza la natura singularitatilor din varietate.