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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2024, том 20, 024, 25 стр. (Mi sigma2026)

Hodge Diamonds of the Landau–Ginzburg Orbifolds

Alexey Basalaevab, Andrei Ionovc

a Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva Str., 119048 Moscow, Russia
b Skolkovo Institute of Science and Technology, 3 Nobelya Str., 121205 Moscow, Russia
c Boston College, Department of Mathematics, Maloney Hall, Fifth Floor, Chestnut Hill, MA 02467-3806, USA

Аннотация: Consider the pairs $(f,G)$ with $f = f(x_1,\dots,x_N)$ being a polynomial defining a quasihomogeneous singularity and $G$ being a subgroup of ${\rm SL}(N,\mathbb{C})$, preserving $f$. In particular, $G$ is not necessary abelian. Assume further that $G$ contains the grading operator $j_f$ and $f$ satisfies the Calabi–Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of $(f,G)$ form a diamond. We identify its topmost, bottommost, leftmost and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms.

Ключевые слова: singularity theory, Landau–Ginzburg orbifolds.

MSC: 32S05, 14J33

Поступила: 12 июля 2023 г.; в окончательном варианте 6 марта 2024 г.; опубликована 25 марта 2024 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2024.024


ArXiv: 2307.01295


© МИАН, 2024