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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
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
Citation:
A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440
Linking options:
https://www.mathnet.ru/eng/mmj154 https://www.mathnet.ru/eng/mmj/v4/i2/p377
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Abstract page: | 870 | Full-text PDF : | 1 | References: | 180 |
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