Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality

被引：2
|
作者：
Dubrovin, Boris
Yang, Di [1 ]
Zagier, Don [2 ,3 ]
机构：
[1] USTC, Sch Math Sci, Jinzhai Rd 96, Hefei 230026, Peoples R China
[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany
[3] Abdus Salaam Int Ctr Theoret Phys, Str Costiera 11, I-34014 Trieste, Italy
来源：
ADVANCES IN MATHEMATICS | 2023年 / 433卷
基金：
中国国家自然科学基金;
关键词：
FJRW invariants; Integrality; Integrable system; Topological ODEs; Wave function; Contents; GROMOV-WITTEN INVARIANTS; TOPOLOGICAL FIELD-THEORY; LANDAU-GINZBURG MODELS; AFFINE WEYL GROUPS; P-SPIN CURVES; INTERSECTION-NUMBERS; MODULI SPACE; TAUTOLOGICAL RELATIONS; FROBENIUS MANIFOLDS; SYSTEMS;
D O I：
10.1016/j.aim.2023.109311
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For each of the simple Lie algebras g = A(l), D-l or E-6, we show that the all-genera one-point FJRW (Fan-Jarvis-Ruan, Witten) invariants of g-type, after multiplication by suitable products of Pochhammer symbols, are the coefficients of an algebraic generating function and hence are integral. Moreover, we find that the all-genera invariants themselves coincide with the coefficients of the unique calibration of the Frobenius manifold of g-type evaluated at a special point. For the A(4) (5-spin) case we also find two other normalizations of the sequence that are again integral and of at most exponential growth, and hence conjecturally are the Taylor coefficients of some period functions. (c) 2023 Elsevier Inc. All rights reserved.
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