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A tale of four theories

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If you have a question about this talk, please contact Dhruv Ranganathan.

I will explain the web of relationships connecting four genus-zero Gromov-Witten theories of snc pairs: logarithmic, orbifold, naive and local. We will see that the orbifold, naive and local theories all coincide, but that their relationship to the logarithmic theory is complicated, involving delicate geometry and combinatorics. Our proofs hinge on a technique – “rank reduction” – which reduces questions about snc divisors to questions about smooth divisors, where the situation is much-better understood. This technique originates from some basic observations on the geometry of the moduli space of logarithmic stable maps, which I will present. This talk is based on joint works with Ranganathan and Battistella-Tseng-You, and on upcoming joint work with Battistella-Ranganathan.

This talk is part of the Algebraic Geometry Seminar series.

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