Tevelev degrees and Hurwitz moduli spaces
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Date
2022-11
Publication Type
Journal Article
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yes
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Abstract
We interpret the degrees which arise in Tevelev's study of scattering amplitudes in terms of moduli spaces of Hurwitz covers. Via excess intersection theory, the boundary geometry of the Hurwitz moduli space yields a simple recursion for the Tevelev degrees (together with their natural two parameter generalisation). We find exact solutions which specialise to Tevelev's formula in his cases and connect to the projective geometry of lines and Castelnuovo's classical count of g1d's in other cases. For almost all values, the calculation of the two parameter generalisation of the Tevelev degree is new. A related count of refined Dyck paths is solved along the way.
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published
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Book title
Volume
173 (3)
Pages / Article No.
479 - 510
Publisher
Cambridge University Press