Seminar in Algebraic Geometry and Number Theory

Abstract: Fano varieties of dimension at most 3 are fully classified into finitely many deformation equivalence classes, and going through the list one can see that none of these have torsion in the third integral cohomology group. We give examples to show that in dimension 4 and up, there exist Fano varieties with such torsion. In dimensions 6 and up, these also give examples of Fano varieties where the strong and weak coniveau filtrations defined by Benoist and Ottem differ. This is joint work with John Christian Ottem.