Alternate Compactifications of Hurwitz Spaces
Contributors: Harris, Joseph D.; Harris, Joseph; Mazur, Barry; Vakil, Ravi
Published: 2012
Language: eng
Description: We construct several modular compactifications of the Hurwitz space H(d,g,h) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the cover to collide to a variable extent, generalizing the spaces of twisted admissible covers of Abramovich, Corti and Vistoli. The resulting spaces are very well-behaved if d is small or if relatively few collisions are allowed. In particular, for d = 2 and 3, they are always well-behaved. For d = 2, we recover the spaces of hyperelliptic curves of Fedorchuk. For d = 3, we obtain new birational models of the space of triple covers.
Notes: Keywords: Birational geometry, Hurwitz space, Maroni, Moduli space, Trigonal curve.

Thesis Ph.D. Harvard University 2012