Luigi Lunardon: Many reasons to fear the Grothendieck ring of varieties

Title: Many reasons to fear the Grothendieck ring of varieties

Speaker: Luigi Lunardon

Abstract: The Grothendieck ring of varieties is an interesting and mysterious ring. In this talk, we introduce it and try to understand something more about its properties. We see how some of its algebraic properties are closely related to many interesting geometric problems. For instance, if the class of the affine line was not a zero-divisor in this ring, it was possible to conclude that the cubic fourfold was rational. Moreover, if this was not enough, we present further geometric reasons to motivate the interest in it. After we have risen your hope that this may actually prove some conjectures, we show that the class of the affine line is a zero-divisor in the Grothendieck ring. Hopefully, even after this shocking revelation, your life will continue as usual; but you will know why this ring is something to be scared of.

Keywords: Grothendieck ring of varieties, class of the affine line, zero d