On Fano schemes of complete intersections

Ciro Ciliberto (1) , M Zaidenberg (2)

1 Università degli Studi di Roma Tor Vergata [Roma] = University of Rome Tor Vergata
2 IF - Institut Fourier

We provide enumerative formulas for the degrees of varieties parameterizing hypersurfaces and complete intersections which contain pro-jective subspaces and conics. Besides, we find all cases where the Fano scheme of the general complete intersection is irregular of dimension at least 2, and for the Fano surfaces we deduce formulas for their holomorphic Euler characteristic.

Mots clés: Hypersurfaces; complete intersections; Fano schemes

Domaines: Géométrie algébrique [math.AG]

Ciro Ciliberto, M Zaidenberg. On Fano schemes of complete intersections. Springer. On Fano schemes of complete intersections, Springer Proc. Math. Stat. 2020 (319), Springer, pp.1-39, 2020, Polynomial Rings and Affine Algebraic Geometry. Selected papers based on the presentations at the conference, PRAAG 2018, Tokyo, Japan, February 12–16, 2018. ⟨hal-02078459v3⟩