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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the monodromy group of everywhere tangent lines to the octic surface in $ {\bf P}\sp 3$


Author: Harry D’Souza
Journal: Proc. Amer. Math. Soc. 104 (1988), 1010-1013
MSC: Primary 14N10
MathSciNet review: 935106
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Abstract: Let $ {S_0}$ be an octic surface in $ {{\mathbf{P}}^3},G = G(1,3)$ = Grassmannian of lines in $ {{\mathbf{P}}^3}$, and $ {\mathbf{J}} = \{ (x,l)\vert x \in l \cap {S_0}\} \subset {S_0} \times G$. Then $ \dim {\mathbf{J}} = 5$. Let $ {\mathbf{L}} = {\{ l\vert l{\text{ is }}everywhere{\text{ tangent to }}{S_0}\} ^ - } \subset G$. Let $ {\pi _2}:{S_0} \times G \to G$ be the projection onto the second factor. We denote its restriction to $ {\mathbf{J}}$ also by $ {\pi _2}$. Then the locus of everywhere tangent lines is $ {\pi _2}({\mathbf{L}})$. In this article we show that the monodromy group of these lines is the full symmetric group.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0935106-6
PII: S 0002-9939(1988)0935106-6
Article copyright: © Copyright 1988 American Mathematical Society



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