Duke Mathematical Journal

Generic strange duality for $K3$ surfaces

Alina Marian and Dragos Oprea
Appendix by Kota Yoshioka

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Abstract

Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier–Mukai techniques. Applications to Brill–Noether theory for sheaves on $K3$ surfaces are also obtained. The appendix, written by Kota Yoshioka, discusses the behavior of the moduli spaces under change of polarization, as needed in the argument.

Article information

Source
Duke Math. J. Volume 162, Number 8 (2013), 1463-1501.

Dates
First available in Project Euclid: 28 May 2013

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1369753568

Digital Object Identifier
doi:10.1215/00127094-2208643

Zentralblatt MATH identifier
06186873

Mathematical Reviews number (MathSciNet)
MR3079253

Subjects
Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}

Citation

Marian, Alina; Oprea, Dragos. Generic strange duality for K 3 surfaces. Duke Mathematical Journal 162 (2013), no. 8, 1463--1501. doi:10.1215/00127094-2208643. http://projecteuclid.org/euclid.dmj/1369753568.


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