Homological projective duality for determinantal varieties

Marcello Bernardara (1) , Michele Bolognesi (2) , Daniele Faenzi (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

In this paper we prove Homological Projective Duality for categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi–Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.

Domaines: Géométrie algébrique [math.AG]

Marcello Bernardara, Michele Bolognesi, Daniele Faenzi. Homological projective duality for determinantal varieties. Advances in Mathematics, 2016, 296, pp.181 - 209. ⟨10.1016/j.aim.2016.04.003⟩. ⟨hal-01816625⟩