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        Shadow of a cubic surface

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        Scriptie-met-bijlages.zip (952.1Kb)
        Publication date
        2020
        Author
        Janssen Groesbeek, R.
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        Summary
        For a smooth cubic surface S in P^3 we can cast a shadow from a point P ∈ S that does not lie on one of the 27 lines of S onto a hyperplane H . The closure of this shadow is a smooth quartic curve. Conversely, from every smooth quartic curve we can reconstruct a smooth cubic surface whose closure of the shadow is this quartic curve. We will also present an algorithm to reconstruct the cubic surface from the bitangents of a quartic curve. The 27 lines of S together with the tangent space T_P S at P are in correspondence with the 28 bitangents or hyperflexes of the smooth quartic shadow curve. Then a short discussion on F-theory is given to relate this geometry to physics.
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        https://studenttheses.uu.nl/handle/20.500.12932/36297
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