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Moscow Mathematical Journal, 2004, Volume 4, Number 2, Pages 377–440
DOI: https://doi.org/10.17323/1609-4514-2004-4-2-377-440
(Mi mmj154)
 

This article is cited in 47 scientific papers (total in 47 papers)

Helix theory

A. L. Gorodentsevab, S. A. Kuleshovbc

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Independent University of Moscow
c N. E. Zhukovskii Military Aviation Engineering University
Full-text PDF Citations (47)
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Abstract: This is a detailed review of helix theory, which describes exceptional sheaves and exceptional bases for derived categories of coherent sheaves on Fano varieties. We explain systematically all basic ideas and constructions related to exceptional objects. Projective spaces and Del Pezzo surfaces are considered especially extensively. Some arithmetic relationships with the mirror symmetry phenomenon are discussed as well. This paper may be considered as a necessary supplement to the book [HuLe], which completely ignores rich structures beyond the zero-dimensional moduli spaces.
Key words and phrases: Exceptional collections, mutations, semiorthogonal decompositions in triangulated categories.
Received: May 30, 2003
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Language: English
Citation: A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440
Citation in format AMSBIB
\Bibitem{GorKul04}
\by A.~L.~Gorodentsev, S.~A.~Kuleshov
\paper Helix theory
\jour Mosc. Math.~J.
\yr 2004
\vol 4
\issue 2
\pages 377--440
\mathnet{http://mi.mathnet.ru/mmj154}
\crossref{https://doi.org/10.17323/1609-4514-2004-4-2-377-440}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2108443}
\zmath{https://zbmath.org/?q=an:1072.14020}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000208594700004}
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  • This publication is cited in the following 47 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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