dc.contributor.advisor Harris, Joseph D. dc.contributor.advisor Bejleri, Dori dc.contributor.advisor Fedorchuk, Maksym dc.contributor.author Han, Changho dc.date.accessioned 2019-12-12T09:02:31Z dc.date.created 2019-05 dc.date.issued 2019-05-09 dc.date.submitted 2019 dc.identifier.citation Han, Changho. 2019. Stable log surfaces, trigonal covers, and canonical curves of genus 4. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029707 * dc.description.abstract We describe a compactification of the moduli space of pairs $(S, C)$ where $S$ is isomorphic to $\PP^1 \times \PP^1$ and $C \subset S$ is a genus 4 curve of class $(3,3)$. We show that the compactified moduli space is a smooth Deligne-Mumford stack with 4 boundary components. We relate our compactification with compactifications of the moduli space $\mathcal M_4$ of genus 4 curves. In particular, we show that our space compactifies the blow-up of the hyperelliptic locus in ${\mathcal M}_4$. We also relate our compactification to a compactification of the Hurwitz space ${\mathcal H}^3_4$ of triple coverings of $\PP^1$ by genus 4 curves. dc.description.sponsorship Mathematics dc.format.mimetype application/pdf dc.language.iso en dash.license LAA dc.subject Algebraic Geometry dc.subject Moduli spaces dc.title Stable log surfaces, trigonal covers, and canonical curves of genus 4 dc.type Thesis or Dissertation dash.depositing.author Han, Changho dc.date.available 2019-12-12T09:02:31Z thesis.degree.date 2019 thesis.degree.grantor Graduate School of Arts & Sciences thesis.degree.grantor Graduate School of Arts & Sciences thesis.degree.level Doctoral thesis.degree.level Doctoral thesis.degree.name Doctor of Philosophy thesis.degree.name Doctor of Philosophy dc.type.material text thesis.degree.department Mathematics thesis.degree.department Mathematics dash.identifier.vireo dc.identifier.orcid 0000-0003-3658-0652 dash.author.email chhan92@hotmail.com
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