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This article is cited in 6 scientific papers (total in 6 papers)
Minimal Gromov–Witten rings
V. V. Przyjalkowski
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
We construct an abstract theory of Gromov–Witten invariants of genus 0
for quantum minimal Fano varieties (a minimal class of varieties
which is natural from the quantum cohomological viewpoint).
Namely, we consider the minimal Gromov–Witten ring: a commutative
algebra whose generators and relations are of the form used in the
Gromov–Witten theory of Fano varieties (of unspecified dimension).
The Gromov–Witten theory of any quantum minimal variety is
a homomorphism from this ring to $\mathbb C$. We prove an abstract
reconstruction theorem which says that this ring is isomorphic
to the free commutative ring generated by ‘prime two-pointed
invariants’. We also find solutions of the differential equation
of type $DN$ for a Fano variety of dimension $N$ in terms
of the generating series of one-pointed Gromov–Witten invariants.
DOI:
https://doi.org/10.4213/im2664
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English version:
Izvestiya: Mathematics, 2008, 72:6, 1253–1272
Bibliographic databases:
     
UDC:
512.772
MSC: 53D45, 14J45, 14N35
Received: 14.05.2007
Citation:
V. V. Przyjalkowski, “Minimal Gromov–Witten rings”, Izv. RAN. Ser. Mat., 72:6 (2008), 203–222; Izv. Math., 72:6 (2008), 1253–1272
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Citing articles on Google Scholar:
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This publication is cited in the following articles:
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Przyjalkowski V., “On Landau-Ginzburg models for Fano varieties”, Communications in Number Theory and Physics, 1:4 (2007), 713–728
-
Nathan Owen Ilten, Jacob Lewis, Victor Przyjalkowski, “Toric degenerations of Fano threefolds giving weak Landau–Ginzburg models”, Journal of Algebra, 374 (2013), 104
-
V. V. Przyjalkowski, “Weak Landau–Ginzburg models for smooth Fano threefolds”, Izv. Math., 77:4 (2013), 772–794
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V. V. Przyjalkowski, C. A. Shramov, “Laurent phenomenon for Landau–Ginzburg models of complete intersections in Grassmannians”, Proc. Steklov Inst. Math., 290:1 (2015), 91–102
-
V. V. Golyshev, D. Zagier, “Proof of the gamma conjecture for Fano 3-folds of Picard rank 1”, Izv. Math., 80:1 (2016), 24–49
-
V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118
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