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4:00 pm Tuesday, February 7, 2012 Algebraic Geometry Seminar: Alternate compactifications of Hurwitz spacesby Anand Deopurkar (Harvard) in HB 227- Moduli spaces of geometrically interesting objects are usually not compact. They need to be compactified by allowing certain carefully chosen degenerations. Often, this can be done in several ways, leading to different birational models that are related in interesting ways. I will describe a range of compactifications of the Hurwitz space H^d_g, which parametrizes d sheeted, simply branched, genus g covers of the projective line. These compactifications are constructed by allowing degenererations where the branch points can collide in a prescribed way, recovering as a particular case the standard compactification by admissible covers. After the general construction, I will focus on the case of d=3. In this case, the above construction gives a sequence of compactifications which contract the boundary divisors in the admissible cover compactification. I will construct a sequence of yet more compactifications that modify the interior, featuring the classical Maroni invariant of trigonal curves.
Submitted by evanmb@gmail.com |