100 citations · 222 across the 43 of their papers we have counts for
46 papers
Solution of the Hurwitz problem with a length-2 partition
Filippo Baroni, Carlo Petronio
In this note we provide a new partial solution to the Hurwitz existence problem for surface branched covers. Namely, we consider candidate branch data with base surface the sphere…
Realizations of certain odd-degree surface branch data
Carlo Petronio
We consider surface branch data with base surface the sphere, odd degree d, three branching points, and two partitions of d of the form (2,...,2,1) and (2,...,2,2h+1). If the third…
Counting surface branched covers
Carlo Petronio, Filippo Sarti
To a branched cover f between orientable surfaces one can associate a certain branch datum D(f), that encodes the combinatorics of the cover. This D(f) satisfies a compatibility co…
Explicit computation of some families of Hurwitz numbers, II
Carlo Petronio
We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching…
Explicit computation of some families of Hurwitz numbers
Carlo Petronio
We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branc…
Elementary solution of an infinite sequence of instances of the Hurwitz problem
Tom Ferragut, Carlo Petronio
We prove that there exists no branched cover from the torus to the sphere with degree 3h and 3 branching points in the target with local degrees (3,...,3), (3,...,3), (4,2,3,...,3)…