## Kyoto Journal of Mathematics

The Kyoto Journal of Mathematics has a long and distinguished history of publishing high-quality and original mathematical research. It publishes research papers and surveys at the forefront of pure mathematics. Advance publication of articles online is available.

A new proof of a theorem of Ramanujam-MorrowVolume 42, Number 1 (2002)
On the uniqueness of solutions of stochastic differential equationsVolume 11, Number 1 (1971)
Foxby equivalence over associative ringsVolume 47, Number 4 (2007)
Some properties of subharmonic functions on complete Riemannian manifolds and their geometric applicationsVolume 44, Number 1 (2004)
Inductive limits of topologies, their direct products, and problems related to algebraic structuresVolume 41, Number 3 (2001)
• Includes:

Kyoto Journal of Mathematics
Coverage: 2010--
ISSN: 2154-3321 (electronic), 2156-2261 (print)

Journal of Mathematics of Kyoto University
Coverage: 1961-2009
ISSN: 0023-608X (print)

Memoirs of the College of Science, University of Kyoto. Series A: Mathematics
Coverage: 1950-1961
ISSN: 0368-8887 (print)

• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1950--
• Access: Articles older than 5 years are open
• Euclid URL: https://projecteuclid.org/kjm

### Featured bibliometrics

MR Citation Database MCQ (2018): 0.53
JCR (2018) Impact Factor: 0.500
JCR (2018) Five-year Impact Factor: 0.533
JCR (2018) Ranking: 249/313 (Mathematics)
Eigenfactor: Kyoto Journal of Mathematics
SJR/SCImago Journal Rank (2018): 0.51

Indexed/Abstracted in: ISI Science Citation Index Expanded, MathSciNet, Scopus, zbMATH

### Featured article

#### A Fock sheaf for Givental quantization

Volume 58, Number 4 (2018)
##### Abstract

We give a global, intrinsic, and coordinate-free quantization formalism for Gromov–Witten invariants and their B-model counterparts, which simultaneously generalizes the quantization formalisms described by Witten, Givental, and Aganagic–Bouchard–Klemm. Descendant potentials live in a Fock sheaf, consisting of local functions on Givental’s Lagrangian cone that satisfy the $(3g-2)$-jet condition of Eguchi–Xiong; they also satisfy a certain anomaly equation, which generalizes the holomorphic anomaly equation of Bershadsky–Cecotti–Ooguri–Vafa. We interpret Givental’s formula for the higher-genus potentials associated to a semisimple Frobenius manifold in this setting, showing that, in the semisimple case, there is a canonical global section of the Fock sheaf. This canonical section automatically has certain modularity properties. When $X$ is a variety with semisimple quantum cohomology, a theorem of Teleman implies that the canonical section coincides with the geometric descendant potential defined by Gromov–Witten invariants of $X$. We use our formalism to prove a higher-genus version of Ruan’s crepant transformation conjecture for compact toric orbifolds. When combined with our earlier joint work with Jiang, this shows that the total descendant potential for a compact toric orbifold $X$ is a modular function for a certain group of autoequivalences of the derived category of $X$.

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