The picard rank conjecture for the hurwitz spaces of degree up to five

Anand Deopurkar; Anand Patel

doi:10.2140/ant.2015.9.459

The picard rank conjecture for the hurwitz spaces of degree up to five

Anand Deopurkar, Anand Patel

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We prove that the rational Picard group of the simple Hurwitz space H_d,g is trivial for d up to five. We also relate the rational Picard groups of the Hurwitz spaces to the rational Picard groups of the Severi varieties of nodal curves on Hirzebruch surfaces.

Original language	English
Pages (from-to)	459-492
Number of pages	34
Journal	Algebra and Number Theory
Volume	9
Issue number	2
DOIs	https://doi.org/10.2140/ant.2015.9.459
Publication status	Published - 2015
Externally published	Yes

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10.2140/ant.2015.9.459

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title = "The picard rank conjecture for the hurwitz spaces of degree up to five",

abstract = "We prove that the rational Picard group of the simple Hurwitz space Hd,g is trivial for d up to five. We also relate the rational Picard groups of the Hurwitz spaces to the rational Picard groups of the Severi varieties of nodal curves on Hirzebruch surfaces.",

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AB - We prove that the rational Picard group of the simple Hurwitz space Hd,g is trivial for d up to five. We also relate the rational Picard groups of the Hurwitz spaces to the rational Picard groups of the Severi varieties of nodal curves on Hirzebruch surfaces.

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KW - Picard group

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The picard rank conjecture for the hurwitz spaces of degree up to five

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