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    Chan, Daniel 2017. 2-Hereditary algebras and almost Fano weighted surfaces. Journal of Algebra, Vol. 478, Issue. , p. 92.
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A RECOLLEMENT APPROACH TO GEIGLE–LENZING WEIGHTED PROJECTIVE VARIETIES

  • BORIS LERNER (a1) and STEFFEN OPPERMANN (a2)
Abstract

We introduce a new method for expanding an abelian category and study it using recollements. In particular, we give a criterion for the existence of cotilting objects. We show, using techniques from noncommutative algebraic geometry, that our construction encompasses the category of coherent sheaves on Geigle–Lenzing weighted projective lines. We apply our construction to some concrete examples and obtain new weighted projective varieties, and analyze the endomorphism algebras of their tilting bundles.

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© 2016 by The Editorial Board of the Nagoya Mathematical Journal  
References
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[BBD] Beilinson, A., Bernstein, J. and Deligne, P., “ Faisceaux pervers [Perverse sheaves] (in French) ”, in Analysis and Topology on Singular Spaces, I (Luminy, 1981), Astérisque, 100 , Soc. Math. France, Paris, 1982, 5–171.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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