The Hurwitz space Picard rank conjecture for \(d > g - 1\)

DOI10.1016/j.aim.2023.109211zbMath1522.14040arXiv2009.10063WikidataQ122971861 ScholiaQ122971861MaRDI QIDQ6135866

Scott Mullane

Publication date: 28 August 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.10063

zbMATH Keywords

intersection theorymoduli spacesPicard groupsHurwitz spacesstrataexact differentials

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Fibrations, degenerations in algebraic geometry (14D06) Picard groups (14C22) Differentials on Riemann surfaces (30F30)

Cites Work

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• The classification of universal Jacobians over the moduli space of curves
• The universal theta divisor over the moduli space of curves
• The second homology group of the mapping class group of an orientable surface
• A bound on the dimensions of complete subvarieties of \({\mathcal M}_ g\).
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Topological recursive relations in \(H^{2g}(\mathcal M_{g,n})\).
• On the Kodaira dimension of the moduli space of curves
• The geometry of the compactification of the Hurwitz scheme
• Towards the homology of Hurwitz spaces
• Compactification of strata of abelian differentials
• The Picard rank conjecture for the Hurwitz spaces of degree up to five
• Strata of differentials of the second kind, positivity and irreducibility of certain Hurwitz spaces
• Divisor classes associated to families of stable varieties, with applications to the moduli space of curves
• Twisted Bundles and Admissible Covers
• Moduli of Trigonal Curves
• Two Moduli Spaces of Calabi–Yau type
• Independence of boundary divisors in the space of admissible covers

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