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Moduli of curves on toric varieties and their stable cohomology

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arxiv 2210.05826 v1 pith:C4GYFIPR submitted 2022-10-11 math.AG math.ATmath.NT

Oishee Banerjee This is my paper · ORCID
classification math.AGmath.ATmath.NT
keywords toriccohomologymodulisigmavarietiesarithmeticbatyrev-manincharacteristics
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abstract

We prove that the cohomology of the moduli space of morphisms of a fixed finite degree from a smooth projective curve $C$ of genus $g$ to a complete simplicial toric variety $\mathbb{P}(\Sigma)$, denoted by the rational polyhedral fan $\Sigma$, stabilizes. As an arithmetic consequence we obtain a resolution of the Batyrev-Manin conjecture for toric varieties over global function fields in all but finitely many characteristics.

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Cited by 1 Pith paper

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  1. A configuration space model for algebraic function spaces

    math.AG 2024-12 reject novelty 6.0 of 10

    A conditional spectral sequence model for algebraic morphism spaces is announced, with an inconsistent stable-range formula and an off-by-two conflict between theorem and proof.

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