Pencils of fermat hypersurfaces and Galois cyclic covers of the projective line

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Let $Z$ be a smooth intersection of two degree $p$ Fermat hypersurfaces in $\mathbb{P}^n$, and let $\pi:X\rightarrow \mathbb{P}^1$ be the pencil of hypersurfaces containing $Z$. We show that the irreducible $\mathbb{Q}$ sublocal systems of $\mathbf{R}^{n-1} \pi_*\underline{\mathbb{Q} }_X$ arise from monodromy of the Galois cyclic covers of $\mathbb{P}^1$. This can be viewed as a higher degree analog of M.\ Reid's result on the correspondence between smooth intersection of two quadrics and hyperelliptic curves.


Type of resource text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2017
Issuance monographic
Language English


Associated with Pan, Donghai
Associated with Stanford University, Department of Mathematics.
Primary advisor Vakil, Ravi
Thesis advisor Vakil, Ravi
Thesis advisor Kemeny, Michael
Thesis advisor Li, Jun, (Mathematician)
Advisor Kemeny, Michael
Advisor Li, Jun, (Mathematician)


Genre Theses

Bibliographic information

Statement of responsibility Donghai Pan.
Note Submitted to the Department of Mathematics.
Thesis Thesis (Ph.D.)--Stanford University, 2017.
Location electronic resource

Access conditions

© 2017 by Donghai Pan
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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