Genuinely ramified maps and monodromy

Authors

Indranil Biswas, Shiv Nadar Institution of Eminence deemed to be University
Manish Kumar, Indian Statistical Institute Bangalore
A. J. Parameswaran, Tata Institute of Fundamental Research, Mumbai

Article Type

Research Article

Publication Title

Journal of Algebra

Abstract

For any genuinely ramified morphism f:Y⟶X between irreducible smooth projective curves we prove that (Y×XY)∖Δ‾ is connected, where Δ⊂Y×XY is the diagonal. Using this result the following are proved: (1) If f is further Morse then the Galois closure is the symmetric group Sd, where d=degree(f). (2) The Galois group of the general projection, to a line, of any smooth curve X⊂Pⁿ of degree d, which is not contained in a hyperplane and contains a non-flex point, is Sd.

First Page

222

Last Page

231

DOI

10.1016/j.jalgebra.2023.12.034

Publication Date

4-15-2024

Comments

Open Access; Green Open Access

Recommended Citation

Biswas, Indranil; Kumar, Manish; and Parameswaran, A. J., "Genuinely ramified maps and monodromy" (2024). Journal Articles. 4809.
https://digitalcommons.isical.ac.in/journal-articles/4809