Paul Aleksander Maugesten

• Maugesten, Paul Aleksander & Moe, Karoline (2019). The 2-Hessian and sextactic points on plane algebraic curves. Mathematica Scandinavica. ISSN 0025-5521. 125(1), p. 13–38. doi: 10.7146/math.scand.a-114715. Full text in Research Archive Show summary

  In an article from 1865, Arthur Cayley claims that given a plane algebraic curve there exists an associated 2-Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the 2-Hessian. In addition, we present a formula for the number of sextactic points on cuspidal curves and tie this formula to the 2-Hessian. Lastly, we consider the special case of rational curves, where the sextactic points appear as zeros of the Wronski determinant of the 2nd Veronese embedding of the curve.

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• Moe, Karoline & Maugesten, Paul Aleksander (2018). Special Weierstrass points and Plücker formulas. Full text in Research Archive
• Maugesten, Paul Aleksander; Ellingsrud, Geir & Moe, Karoline (2017). Sextactic Points on Plane Algebraic Curves. Universitetet i Oslo. Full text in Research Archive Show summary

  In this thesis we consider sextactic points on plane algebraic curves and a 2-Hessian curve that identifies these points. This curve was first established by Cayley, and we prove that Cayley's 2-Hessian is wrong. Moreover, we correct his mistakes and give the correct defining polynomial of the 2-Hessian curve. In addition, we present a formula for the number of sextactic points on a cuspidal curve.

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