Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles

1994/12/14 by Ugo Bruzzo, Bruzzo, Ugo, Antony Maciocia +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9412014

8 pages, AMSLaTeX, no figures

arxiv created 1994/12/14 · openalex publication_date 1994/12/14 · arxiv updated 2015/06/30 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces X the punctual Hilbert schemes \Hilbⁿ(X) can be identified, for all n≥ 1, with moduli spaces of Gieseker stable vector bundles on X of rank 1+2n. We also introduce a new Fourier-Mukai type transform for such surfaces.

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