Comments on the ELSV compactification of Hurwitz stacks

Bashar Dudin (1)

1 LMM - Laboratoire Manceau de Mathématiques

We revisit Ekedahl, Lando, Shapiro and Vainshtein's compactification of the stack of simply ramified covers of the projective line except for a fixed ramification profile above infinity. In particular we draw a connection with the Harris and Mumford stack of admissible covers showing that the boundary of the ELSV compactification appears as a contraction of the boundary of the stack of admissible covers. This lays the needed foundations for a combinatoral interpretation of boundary points of the ELSV compactification

Mots clés: Hurwitz stacks. ELSV formula. Admissible covers; Hurwitz stacks. ELSV formula. Admissible covers.

Domaines: Géométrie algébrique [math.AG]

Bashar Dudin. Comments on the ELSV compactification of Hurwitz stacks. 2014. ⟨hal-00705862v2⟩