Examples of smooth surfaces in $\mathbb{P}^3$ which are Ulrich--wild
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 667-677
https://doi.org/10.4134/BKMS.b160257
Published online March 31, 2017
Gianfranco Casnati
Politecnico di Torino
Abstract : Let $F\subseteq\mathbb{P}^3$ be a smooth surface of degree $3\le d\le 9$ whose equation can be expressed as either the determinant of a $d\times d$ matrix of linear forms, or the pfaffian of a $(2d)\times (2d)$ matrix of linear forms. In this paper we show that $F$ supports families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.
Keywords : vector bundle, Ulrich bundle, linear determinantal, linear pfaffian, representation type
MSC numbers : Primary 14J60; Secondary 14J70
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