Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(2): 667-677

Online first article January 17, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160257

Copyright © The Korean Mathematical Society.

Examples of smooth surfaces in $\mathbb{P}^3$ which are Ulrich--wild

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