Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Andreas Krug
  • Jørgen Vold Rennemo

Organisationseinheiten

Externe Organisationen

  • University of Oslo
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Details

OriginalspracheEnglisch
Seiten (von - bis)158-174
Seitenumfang17
FachzeitschriftMathematische Nachrichten
Jahrgang295
Ausgabenummer1
Frühes Online-Datum14 Dez. 2021
PublikationsstatusVeröffentlicht - 31 Jan. 2022

Abstract

For X a smooth quasi-projective variety and (Formula presented.) its associated Hilbert scheme of n points, we study two canonical Fourier–Mukai transforms (Formula presented.), the one along the structure sheaf and the one along the ideal sheaf of the universal family. For (Formula presented.), we prove that both functors admit a left inverse. This means in particular that both functors are faithful and injective on isomorphism classes of objects. Using another method, we also show in the case of an elliptic curve that the Fourier–Mukai transform along the structure sheaf of the universal family is faithful and injective on isomorphism classes. Furthermore, we prove that the universal family of (Formula presented.) is always flat over X, which implies that the Fourier–Mukai transform along its structure sheaf maps coherent sheaves to coherent sheaves.

ASJC Scopus Sachgebiete

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Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points. / Krug, Andreas; Rennemo, Jørgen Vold.
in: Mathematische Nachrichten, Jahrgang 295, Nr. 1, 31.01.2022, S. 158-174.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Krug A, Rennemo JV. Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points. Mathematische Nachrichten. 2022 Jan 31;295(1):158-174. Epub 2021 Dez 14. doi: 10.1002/mana.201900351
Krug, Andreas ; Rennemo, Jørgen Vold. / Some ways to reconstruct a sheaf from its tautological image on a Hilbert scheme of points. in: Mathematische Nachrichten. 2022 ; Jahrgang 295, Nr. 1. S. 158-174.
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