The Irreducibility and Monodromy of Some Families of Linear Series with Imposed Ramifications

Xiaoyu Hu ()
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Xiaoyu Hu: Department of Mathematical Sciences, Tsinghua University, Haidian District, Beijing 100084, China

Mathematics, 2025, vol. 13, issue 3, 1-23

Abstract: Suppose that the adjusted Brill–Noether number is zero; we prove that there exists a family of twice-marked smooth projective curves such that the family of linear series with two imposed ramification conditions is irreducible. Moreover, under certain conditions, we show that the monodromy group contains the alternating group. In the case r = 1 , the monodromy group is the full symmetric group.

Keywords: algebraic curves; linear series; ramification; monodromy; Brill–Noether theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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