On symplectic homology of the complement of a positive normal crossing divisor in a projective variety
Abstract/Contents
- Abstract
- This dissertation studies how symplectic homology of the complement of the smooth zero set $D$ of a section of a positive line bundle $\cL$ over a projective variety $(X, J)$ changes as $D$ degenerates to a normal crossing divisor $D_{\mbox{sing}}$ with two smooth connected components. By analyzing the pluri-subharmonic functions obtained from a metric on $\cL$, we show that the change in the Weinstein structure of the complement is characterized by handle removals along the unstable submanifolds of critical points in a small neighborhood of the set of singular points of $D_{\mbox{sing}}.$ Parallel to work by Bourgeois-Eckholm-Eliashberg (\cite{BEE}), we construct a chain complex from the removed unstable submanifolds such that its homology completes the Viterbo transfer map in a long exact sequence. The effect of divisor degeneration on symplectic homology of the complement is then essentially reflected by the $A_\infty$ structure of a collection of Lagrangian spheres on $D$, which are the boundary at infinity of the removed unstable submanifolds.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Nguyen, Khoa Lu |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Eliashberg, Y, 1946- |
| Thesis advisor | Eliashberg, Y, 1946- |
| Thesis advisor | Galatius, Søren, 1976- |
| Thesis advisor | Ionel, Eleny |
| Advisor | Galatius, Søren, 1976- |
| Advisor | Ionel, Eleny |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Khoa Lu Nguyen. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Khoa Lu Nguyen
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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