Shadow of a cubic surface
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.