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Transactions of the American Mathematical Society

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Invariants and projections of six lines in projective space


Author: Dana R. Vazzana
Journal: Trans. Amer. Math. Soc. 353 (2001), 2673-2688
MSC (2000): Primary 14L24; Secondary 14Q10
DOI: https://doi.org/10.1090/S0002-9947-01-02742-8
Published electronically: January 18, 2001
MathSciNet review: 1828467
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Abstract:

Given six lines in $\mathbf{P}^3$, quartics through the six lines define a map from $\mathbf{P}^3$ to $\mathbf{P}^4$, and the image of this map is described in terms of invariants of the six lines. The map can be interpreted as projection of the six lines, and this permits a description of the canonical model of the octic surface which is given by points which project the lines so that they are tangent to a conic. We also define polarity for sets of six lines, and discuss the above map in the case of a self-polar set of lines and in the case of six lines which form a ``double-sixer'' on a cubic surface.


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Additional Information

Dana R. Vazzana
Affiliation: Department of Mathematics and Computer Science, Truman State University, Kirksville, Missouri 63501
Email: dvazzana@truman.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02742-8
Keywords: Algebraic geometry, invariant theory
Received by editor(s): July 25, 1999
Published electronically: January 18, 2001
Additional Notes: The author would like to thank Igor Dolgachev for his invaluable assistance in producing this research.
Article copyright: © Copyright 2001 American Mathematical Society

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