On a Certain Scroll Associated with a Net of Quadrics


Affiliations

  • Patna Science College, Patna, India

Abstract

In a paper published in the Bulletin of the Calcutta Mathematical Society (Chariar, 1944) the author discussed a scroll generated by lines whose polars with respect to a net of quadrics are concurrent. It was proved that the surface R generated by such lines is of order 9, having the Jacobian curve r of the net as a multiple curve. In this paper some other properties of R are obtained. It is found that R is generated by trisectants of r which is the only multiple curve on R. It is also found that r is a multiple curve of order three on R whose genus is 10. Lines whose polars with respect to four quadrics not belonging to a net, are concurrent are also discussed.

Subject Discipline

Mathematical Sciences

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