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A Survey of Ulrich Bundles

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Analytic and Algebraic Geometry

Abstract

The purpose of this article is to serve as an introduction to Ulrich bundles for interested readers. We discuss the origins of the study of Ulrich bundles, their elementary properties, and we give an exposition of the known results in their classification on various kinds of smooth projective varieties. As an illustration of a method recently used by Marta Casanellas and Robin Hartshorne for the classification of Ulrich bundles on a cubic surface, we classify the stable Ulrich bundles on a smooth quartic surface in ℙ3 of Picard number 2 by first Chern class.

The author was supported by TÜBİTAK scholarship 2232. He would also like to thank the Tata Institute of Fundamental Research and the Institut des Hautes Études Scientifiques, where he conducted research on Ulrich bundles on K3 surfaces.

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Emre Coskun

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  1. Emre Coskun
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Correspondence to Emre Coskun .

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Editors and Affiliations

  1. Department of Mathematics, IISER Tirupati, Tirupati, Andhra Pradesh, India

    Anilatmaja Aryasomayajula

  2. School of Mathematics, Tata Institute of Fundamental Research, Mumbai, Maharashtra, India

    Indranil Biswas

  3. School of Mathematics and Statistics, University of Hyderabad, Hyderabad, Telangana, India

    Archana S. Morye

  4. School of Mathematics, Tata Institute of Fundamental Research, Mumbai, Maharashtra, India

    A. J. Parameswaran

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Coskun, E. (2017). A Survey of Ulrich Bundles. In: Aryasomayajula, A., Biswas, I., Morye, A.S., Parameswaran, A.J. (eds) Analytic and Algebraic Geometry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5648-2_6

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