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Sbornik: Mathematics, 2007, Volume 198, Issue 9, Pages 1325–1340
DOI: https://doi.org/10.1070/SM2007v198n09ABEH003885 (Mi sm3913) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties

V. V. Przyjalkowski

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (417 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM2007v198n09ABEH003885
Abstract: Givental's theorem for complete intersections in smooth toric varieties is generalized to Fano varieties. The Gromov–Witten invariants are found for Fano varieties of dimension $\geqslant3$ that are complete intersections in weighted projective spaces or singular toric varieties. A generalized Riemann–Roch equation is also obtained for such varieties. As a consequence, the counting matrices of smooth Fano threefolds with Picard group $\mathbb Z$ and anticanonical degrees 2, 8, and 16 are calculated.
Bibliography: 29 titles.
Received: 18.01.2005 and 07.09.2006
Russian version:
Matematicheskii Sbornik, 2007, Volume 198, Number 9, Pages 107–122
DOI: https://doi.org/10.4213/sm3913
Bibliographic databases:
Document Type: Article
UDC: 512.772
MSC: 14J45, 14M25, 11F23
Language: English
Original paper language: Russian
Citation: V. V. Przyjalkowski, “Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties”, Mat. Sb., 198:9 (2007), 107–122; Sb. Math., 198:9 (2007), 1325–1340
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:574
    Russian version PDF:254
    English version PDF:23
    References:74
    First page:4
     
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