Togliatti systems and Galois coverings

Emilia Mezzetti

Università di Trieste

In two articles, published in 1929 and in 1946, Eugenio Togliatti introduced and studied an example of rational surface in the 5-dimensional projective space satisfying a Laplace equation. In geometric terms this translates in the property of having all osculating spaces of dimension less than expected. This example has led to the notion of Togliatti system, which has been much studied recently, also because of its interesting connections with the algebraic property called weak Lefschetz property. In the talk, after introducing these notions, I will speak of a new class of examples of Togliatti systems, associated via apolarity to some cyclic Galois coverings. Joint work with Rosa Maria Mirò Roig.