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Register a new userAn algebraic proof of the hyperplane property of the genus one GW-invariants of quintics
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Li-Zingers hyperplane theorem states that the genus one GW-invariants of the quintic threefold is the sum of its reduced genus one GW-invariants and 1/12 multiplies of its genus zero GW-invariants. We apply the Guffin-Sharpe-Wittens theory (GSW theory) to give an algebro-geometric proof of the hyperplane theorem, including separation of contributions and computation of 1/12.
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The solutions to the Kadomtsev-Petviashvili equation that arise from a fixed complex algebraic curve are parametrized by a threefold in a weighted projective space, which we name after Boris Dubrovin. Current methods from nonlinear algebra are applied to study parametrizations and defining ideals of Dubrovin threefolds. We highlight the dichotomy between transcendental representations and exact algebraic computations. Our main result on the algebraic side is a toric degeneration of the Dubrovin threefold into the product of the underlying canonical curve and a weighted projective plane.
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We propose a conjectural explicit formula of generating series of a new type for Gromov--Witten invariants of $mathbb{P}^1$ of all degrees in full genera.
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