turkmath.org

In this talk we discuss the problem of classifying complex non-special simple quartics up to equisingular deformation by reducing the problem to an arithmetical problem about lattices. On this arithmetical side, after applying Nikulin's existence theorem, our computation based on the Miranda-Morrison's theory computing the genus groups. We give a complete description of equisingular strata of non-special simple quartics. First we recall fundamentals of Nikulin's theory of discriminant forms and lattice extensions and give a brief introduction to Miranda-Morrison's theory and recast some of their results in a form more suitable for our computations. Then we recall the notion of abstract homological types and arithmetical reduction of classification problem. Finally we give ideas of the proof of our principal result.