Non-Abelian Lefschetz hyperplane theorems
Abstract/Contents
- Abstract
- Let X be a smooth variety over the complex numbers, and let D be an ample divisor in X. For which spaces Y does every map from D to Y extend uniquely to a map X to Y? Our main result, proved via positive characteristic methods, is the following: if dim(X) > 2, Y is smooth, the cotangent bundle of Y is nef, and dim(Y) < dim(D), every such map extends. Taking Y to be the classifying space of a finite group BG, the moduli space of pointed curves M_g, n, the moduli space of principally polarized Abelian varieties A_g, certain period domains, and various other moduli spaces, one obtains many new and classical Lefschetz hyperplane theorems. We also prove many other such extension theorems, and develop general techniques for recognizing spaces Y for which these sorts of Lefschetz theorems hold.
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 | Litt, Daniel | |
|---|---|---|
| Associated with | Stanford University, Department of Mathematics. | |
| Primary advisor | Vakil, Ravi | |
| Thesis advisor | Vakil, Ravi | |
| Thesis advisor | Conrad, Brian | |
| Thesis advisor | Galatius, Søren, 1976- | |
| Advisor | Conrad, Brian | |
| Advisor | Galatius, Søren, 1976- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Daniel Litt. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Daniel Abraham Litt
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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