TY - JOUR

T1 - Orbifold Milnor lattice and orbifold intersection form

AU - Ebeling, Wolfgang

AU - Gusein-Zade, Sabir M.

N1 - Funding information: Partially supported by DFG (Eb 102/8-1). The work of Sabir M. Gusein-Zade (Sects. 2, 4, 6 and 7) was supported by the Grant 16-11-10018 of the Russian Science Foundation.

PY - 2018/3

Y1 - 2018/3

N2 - For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology group. It is considered as the main object of the quantum singularity theory (FJRW-theory). We define orbifold versions of the monodromy operator on the quantum (co)homology group, of the Milnor lattice, of the Seifert form and of the intersection form. We also describe some symmetry properties of invariants of invertible polynomials refining the known ones.

AB - For a germ of a quasihomogeneous function with an isolated critical point at the origin invariant with respect to an appropriate action of a finite abelian group, H. Fan, T. Jarvis, and Y. Ruan defined the so-called quantum cohomology group. It is considered as the main object of the quantum singularity theory (FJRW-theory). We define orbifold versions of the monodromy operator on the quantum (co)homology group, of the Milnor lattice, of the Seifert form and of the intersection form. We also describe some symmetry properties of invariants of invertible polynomials refining the known ones.

KW - 14R20

KW - 32S05

KW - 57R18

KW - 58K65

KW - 58K70

UR - http://www.scopus.com/inward/record.url?scp=85020626823&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1607.08740

DO - 10.48550/arXiv.1607.08740

M3 - Article

AN - SCOPUS:85020626823

VL - 155

SP - 335

EP - 353

JO - Manuscripta mathematica

JF - Manuscripta mathematica

SN - 0025-2611

IS - 3-4

ER -