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arXiv · 2106.01206

Bifurcations of embedded curves and towards an extension of Taubes' Gromov invariant to Calabi-Yau 3-folds

Shaoyun Bai·Mohan Swaminathan
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Abstract

We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau $3$-folds, which can be viewed as an extension of Taubes' Gromov invariant. The construction depends on a detailed study of bifurcations of moduli spaces of embedded pseudo-holomorphic curves which is partially motivated by Wendl's recent solution of Bryan--Pandharipande's super-rigidity conjecture.

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Shaoyun Bai, Mohan Swaminathan. 2021-06-02. Bifurcations of embedded curves and towards an extension of Taubes' Gromov invariant to Calabi-Yau 3-folds. https://arxiv.org/abs/2106.01206

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