16 feb 2022 -- 17:00
Geometry in Como - online
Abstract.
The 19-dimensional moduli space $F_g$ of polarized K3 surfaces of genus $g$ (and degree $2g-2$) is known to be unirational for some low values of $g$, due to results by Mukai, Nuer, Farkas and Verra. However, only for very few values of $g$ the construction of unirationality provides a computer-implementable algorithm to determine the equations of the general member of $F_g$. We shall present the relations between some K3 surfaces and some special cubic fourfolds and describe a procedure to determine explicitly the equations of the general K3 surface of genus $g$ as a function of a number of specific independent variables. This procedure can be easily implemented in Macaulay2 and, in particular, it yields the explicit unirationality of $F_g$ for $g=11,14,20,22$. This is based on joint works with Giovanni Staglianò.