Symmetric Differential Forms on the Barth Sextic Surface

Author: 
Date created: 
2015-04-14
Identifier: 
etd8972
Keywords: 
Differential forms
Graded modules
Coherent algebraic sheaves
Genus zero curves
Abstract: 

This thesis concerns the existence of regular symmetric differential 2-forms on the Barth sextic surface, here denoted by X. This surface has 65 nodes, the maximum possible for a sextic hypersurface in P^3. This project is motivated by a recent work of Bogmolov and De Oliveira where it is shown that a hypersurface in P^3 with many nodes compared to its degree contains only finitely many genus zero and one curves. We find that there are symmetric differential 2-forms on X that are regular everywhere outside the nodes. We also find that none of these extend to a regular form on the minimal resolution of X. Using these forms we can prove that any genus 0 curve on X must pass through at least one node, and we determine the curves passing through just a select set of nodes.

Document type: 
Thesis
Rights: 
Copyright remains with the author. The author granted permission for the file to be printed, but not for the text to be copied and pasted.
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Senior supervisor: 
Nils Bruin
Department: 
Science:
Thesis type: 
(Thesis) M.Sc.
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