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Tangent planes to discriminant surfaces

Weitenberg, E. (2010) Tangent planes to discriminant surfaces. Bachelor's Thesis, Mathematics.

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Abstract

The Rijksuniversiteit Groningen has a number of string models of discriminant surfaces. In this thesis we study these discriminant surfaces and identify the models. We begin by defining the discriminant for arbitrary polynomials and we recall some of its properties. Next, we study the family of tangent planes to such discriminant surfaces. A result is proved that expresses them in terms of the polynomial that defines the discriminant surface itself. This results in a ruling for discriminant surfaces corresponding to a certain family of polynomials. For the surfaces depicted by the string models, it turns out that the ruling is the set of tangent lines to one singular curve in the surface. Finally, we identify the rulings and each of these singular curves in each of the string models.

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 07:30
Last Modified: 15 Feb 2018 07:30
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/8977

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