Seminario - F-signature function of quotient singularities

il giorno 13 Novembre alle ore 15,30 in aula Anile il Prof. Alessio Caminata (Universita' di Neuchatel) terra' un seminario dal titolo:
F-signature function of quotient singularities

Abstract: The F-signature function is a numerical function defined for a Noetherian local ring R of positive characteristic by looking at the splitting behaviour of the Frobenius endomorphism. So far, most of the efforts have been devoted to studying the leading term of the function, called F-signature and denoted by s(R). Despite being a coarser invariant, s(R) already encodes a significant amount of information about the ring and its singularities. On the other hand, the techniques that allow to determine s(R) often do not allow to compute the whole F-signature function which remains quite mysterious and it is known only for very specific classes of rings. In the first part of the talk, we will review the state-of-the-art on the F-signature function, in particular its connection with the Hilbert-Kunz function, another important numerical function which is a positive characteristic analogous of the classic Hilbert-Samuel function. In the second part, we will concentrate on invariant rings under the action of a finite group, the so-called quotient singularities, and investigate the behaviour of the F-signature function for these rings. This is a joint work with A. De Stefani.