Integral Structure for Simple Singularities
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative $K$-group defined through the Berglund–Hübsch dual of the corresponding singularity.
Keywords: simple singularities, period map, mirror symmetry, topological K-theory.
@article{SIGMA_2020_16_a80,
     author = {Todor Milanov and Chenghan Zha},
     title = {Integral {Structure} for {Simple} {Singularities}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a80/}
}
TY  - JOUR
AU  - Todor Milanov
AU  - Chenghan Zha
TI  - Integral Structure for Simple Singularities
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2020
VL  - 16
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a80/
LA  - en
ID  - SIGMA_2020_16_a80
ER  - 
%0 Journal Article
%A Todor Milanov
%A Chenghan Zha
%T Integral Structure for Simple Singularities
%J Symmetry, integrability and geometry: methods and applications
%D 2020
%V 16
%U http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a80/
%G en
%F SIGMA_2020_16_a80
Todor Milanov; Chenghan Zha. Integral Structure for Simple Singularities. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a80/

[1] Arnol'd V.I., Guseĭn-Zade S. M., Varchenko A. N., Singularities of differentiable maps, v. II, Monographs in Mathematics, 83, Monodromy and asymptotics of integrals, Birkhäuser Boston, Inc., Boston, MA, 1988 | DOI | MR | Zbl

[2] Atiyah M., Segal G., “On equivariant Euler characteristics”, J. Geom. Phys., 6 (1989), 671–677 | DOI | MR | Zbl

[3] Berglund P., Hübsch T., “A generalized construction of mirror manifolds”, Nuclear Phys. B, 393 (1993), 377–391, arXiv: hep-th/9201014 | DOI | MR | Zbl

[4] Chiodo A., Iritani H., Ruan Y., “Landau–Ginzburg/Calabi–Yau correspondence, global mirror symmetry and Orlov equivalence”, Publ. Math. Inst. Hautes Études Sci., 119 (2014), 127–216, arXiv: 1201.0813 | DOI | MR | Zbl

[5] Chiodo A., Nagel J., “The hybrid Landau–Ginzburg models of Calabi–Yau complete intersections”, Topological Recursion and its Influence in Analysis, Geometry, and Topology, Proc. Sympos. Pure Math., 100, Amer. Math. Soc., Providence, RI, 2018, 103–117, arXiv: 1506.02989 | DOI | MR | Zbl

[6] Fan H., Jarvis T., Ruan Y., “The Witten equation, mirror symmetry, and quantum singularity theory”, Ann. of Math., 178 (2013), 1–106, arXiv: 0712.4021 | DOI | MR | Zbl

[7] Frenkel E., Givental A., Milanov T., “Soliton equations, vertex operators, and simple singularities”, Funct. Anal. Other Math., 3 (2010), 47–63, arXiv: 0909.4032 | DOI | MR | Zbl

[8] Givental A. B., “Gromov–Witten invariants and quantization of quadratic Hamiltonians”, Mosc. Math. J., 1 (2001), 551–568, arXiv: math.AG/0108100 | DOI | MR | Zbl

[9] Givental A. B., “Semisimple Frobenius structures at higher genus”, Int. Math. Res. Not., 2001 (2001), 1265–1286, arXiv: math.AG/0008067 | DOI | MR | Zbl

[10] Givental A. B., Milanov T. E., “Simple singularities and integrable hierarchies”, The Breadth of Symplectic and Poisson Geometry, Progr. Math., 232, Birkhäuser Boston, Boston, MA, 2005, 173–201, arXiv: math.AG/0307176 | DOI | MR

[11] Hertling C., Frobenius manifolds and moduli spaces for singularities, Cambridge Tracts in Mathematics, 151, Cambridge University Press, Cambridge, 2002 | DOI | MR | Zbl

[12] Iritani H., “An integral structure in quantum cohomology and mirror symmetry for toric orbifolds”, Adv. Math., 222 (2009), 1016–1079, arXiv: 0903.1463 | DOI | MR | Zbl

[13] Kontsevich M., “Intersection theory on the moduli space of curves and the matrix Airy function”, Comm. Math. Phys., 147 (1992), 1–23 | DOI | MR | Zbl

[14] Krawitz M., FJRW rings and Landau–Ginzburg mirror symmetry, Ph.D. Thesis, University of Michigan, 2010 | MR

[15] Minami H., “A Künneth formula for equivariant $K$-theory”, Osaka Math. J., 6 (1969), 143–146 | MR | Zbl

[16] Saito K., On periods of primitive integrals, I, Preprint, Research Institute for Mathematical Sciences, Kyoto University, 1982

[17] Satake I., “On a generalization of the notion of manifold”, Proc. Nat. Acad. Sci. USA, 42 (1956), 359–363 | DOI | MR | Zbl

[18] Segal G., “Equivariant $K$-theory”, Inst. Hautes Études Sci. Publ. Math., 1968, 129–151 | DOI | MR | Zbl

[19] Teleman C., “The structure of 2D semi-simple field theories”, Invent. Math., 188 (2012), 525–588, arXiv: 0712.0160 | DOI | MR | Zbl