Thesis advisor: Dawei Chen / We study the classes of several loci in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves and over the moduli space of genus g curves with n marked points. In particular we consider the class of the closure in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves with n marked points of the codimension n locus where the n marked points are zeros of the k-differential. We compute this class when n=2 and provide a recursive formula for it when n>2. Moreover, when n=1 and k=1,2 we show its rigidity and extremality in the pseudoeffective cone. We also compute the classes of the closures in the projectivization of the k-th Hodge bundle over the moduli space of genus g curves of the loci where the k-differential has a zero at a Brill-Noether special point. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
| Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_109066 |
| Date | January 2021 |
| Creators | Gheorghita, Iulia |
| Publisher | Boston College |
| Source Sets | Boston College |
| Language | English |
| Detected Language | English |
| Type | Text, thesis |
| Format | electronic, application/pdf |
| Rights | Copyright is held by the author, with all rights reserved, unless otherwise noted. |
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