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May 9, 2018 at 19:32 vote accept Kelyane Abreu
May 9, 2018 at 18:19 answer added Jason Starr timeline score: 3
May 9, 2018 at 17:24 comment added Kelyane Abreu Yes, I am excluding constant morphisms. Thank you
May 9, 2018 at 16:33 comment added Jason Starr I assume that you are excluding constant morphisms. You can produce a dominant morphism as the composition of any dominant, finite morphism $q:C\to \mathbb{P}^1$ from a smooth curve $C$ of genus $g$ and the normalization $\nu:\mathbb{P}^1\to B$ of an irreducible curve $B$ of arithmetic genus $g$ and geometric genus $0$, e.g., a curve with $g$ nodes.
May 9, 2018 at 16:18 history asked Kelyane Abreu CC BY-SA 4.0