Jumping pairs of Steiner bundles. (English) Zbl 1435.14040

Arrondo, Enrique; Marchesi, Simone

Forum Math. 27, No. 6, 3233-3267 (2015).

Summary: In this work we introduce the definition of Schwarzenberger bundle on a Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept of jumping pair for a Steiner bundle on a Grassmannian. After studying the jumping locus variety and bounding its dimension, we give a complete classification of Steiner bundles with jumping locus of maximal dimension, which all are Schwarzenberger bundles.

MSC:

14J60	Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14M15	Grassmannians, Schubert varieties, flag manifolds
14N05	Projective techniques in algebraic geometry

Keywords:

Steiner bundle; Schwarzenberger bundle; Grassmannian