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- W4387560781 abstract "This paper determines the full derived deformation theory of certain smooth rational curves C in Calabi-Yau 3-folds, by determining all higher A_infty-products in its controlling DG-algebra. This geometric setup includes very general cases where C does not contract, cases where the curve neighbourhood is not rational, all known simple smooth 3-fold flops, and all known divisorial contractions to curves. As a corollary, it is shown that the noncommutative deformation theory of C can be described as a superpotential algebra derived from what we call free necklace polynomials, which are elements in the free algebra obtained via a closed formula from combinatorial gluing data. The description of these polynomials, together with the above results, establishes a suitably interpreted string theory prediction due to Ferrari, Aspinwall-Katz and Curto-Morrison. Perhaps most significantly, the main results give both the language and evidence to finally formulate new contractibility conjectures for rational curves in CY 3-folds, which lift Artin's celebrated results from surfaces." @default.
- W4387560781 created "2023-10-12" @default.
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- W4387560781 date "2023-10-09" @default.
- W4387560781 modified "2023-10-13" @default.
- W4387560781 title "Derived deformation theory of crepant curves" @default.
- W4387560781 doi "https://doi.org/10.48550/arxiv.2310.06133" @default.
- W4387560781 hasPublicationYear "2023" @default.
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