Non-Ulrich representation type

Daniele Faenzi (1) , Francesco Malaspina (2) , Giangiacomo Sanna (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Polito - Politecnico di Torino = Polytechnic of Turin
3 FU Berlin - Institut für Mathematik

We show that a smooth projective non-degenerate arithmetically Cohen-Macaulay subvariety X of P^N infinite Cohen-Macaulay type becomes of finite Cohen-Macaulay type by removing Ulrich bundles if and only if N = 5 and X is a quartic scroll or the Segre product of a line and a plane. In turn, we give a complete and explicit classification of ACM bundles over these varieties.

Mots clés: Ulrich sheaves; representation type of algebras; Cohen-Macaulay sheaves and modules; Ulrich sheaves

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

Daniele Faenzi, Francesco Malaspina, Giangiacomo Sanna. Non-Ulrich representation type. 2021. ⟨hal-02173257v2⟩