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Mullane, Scott. “Adventures in the canonical bundle on curves”, Boston College, 2016. http://hdl.handle.net/2345/bc-ir:107220.
Abstract
We investigate the birational geometry of Mg and Mg,n through the use of the strata of abelian differentials and the strata of zero residue differentials that form affine invariant submanifolds in the strata. We compute the class of codimension one subvarieties in Mg and Mg,n coming from these strata and study their birational significance.