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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.
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 applie
In our previous work, we provided an algebraic proof of the Zingers comparison formula between genus one Gromov-Witten invariants and reduced invariants when the target space is a complete intersection of dimension two or three in a projective space.
In this paper we prove that the etale sheafification of the functor arising from the quotient of an algebraic supergroup by a closed subsupergroup is representable by a smooth superscheme.
Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds
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.