Moduli Space of A-Infinity Structures and Nonreduced Curves of Genus 0
| dc.contributor.advisor | Polishchuk, Alexander | |
| dc.contributor.author | Zhang, Wei | |
| dc.date.accessioned | 2022-10-04T19:42:48Z | |
| dc.date.available | 2022-10-04T19:42:48Z | |
| dc.date.issued | 2022-10-04 | |
| dc.description.abstract | In this thesis, we study $A_\infty$-structures arising from derived categories of certain algebraic curves. More precisely, we consider pairs $(\mathcal{O}_C,\mathcal{O}_D)$, where $C$ is an irreducible projective curve over a field $k$ with $H^0(C,\mathcal{O}_C)=k$ and $H^1(C,\mathcal{O}_C)=0$, and $D\sub C$ is a Cartier divisor of degree $2$, supported at one point. They satisfy certain categorical properties encoded in the notion of an $R$-pair (of genus $0$), $(E,F)$, which we will define. In particular, $E$ is exceptional and $F$ is $R$-spherical which is a version of the notion of a $1$-spherical object defined in the work of Seidel and Thomas. The main result of this thesis is to prove the equivalence between the moduli of the $R$-pairs and that of certain filtered algebras which permit a simpler description, i.e. given by the quotient stack of a closed subscheme of $\mathbb{A}^3$ for some action of $\mathbb{G}_a$. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/27614 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.title | Moduli Space of A-Infinity Structures and Nonreduced Curves of Genus 0 | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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