- 25 Mag 2022
A theorem of Mather and Yau
After several “preparation works” by Mather, in 1982 Mather and Yau stated and proved a fundamental result concerning the reconstruction of a hypersurface (up to biholomorphic equivalence) from the corresponding algebra. In particular, in the algebraic setting, two Jacobian algebras are isomorphic if and only if the corresponding hypersurfaces are projectively equivalent. We will give an idea of the original proof, also introducing several objects that are necessary for it. In conclusion, we will focus on some important applications of this result, as the study of the so-called “Generic Torelli Problem”, as done for example by Carlson-Griffiths and Donagi.