Seminário de Geometria Algébrica
Sexta 07/06 às 11h sala 222
Palestrante: Pedro Henrique dos Santos (IMECC)
Título: A quiver description of some nested Hilbert schemes of points
Hilbert schemes, introduced by Grothendieck, are a fundamental example of the notion of moduli space of geometric structures. The work of Nakajima on Hilbc
(A ) has been the basis for researches aiming to understand the properties of Hilbert schemes of other surfaces or in higher dimensions. For instance, von Flach, Jardim and Lanza proved that the nested Hilbert scheme of points on Ais a quiver variety, and Bartocci, Bruzzo, Lanza and Rava provided a quiver description of the Hilbert scheme of points of the total space of the line bundles OP1 (−n). This seminar is based on the paper [6] (joint work with U. Bruzzo and V. Lanza) and on my PhD thesis. Our main result was to prove that the scheme Hilbc ,c(tot(OP1 (−n))) can be seen as a moduli space of representations of a quiver with relations, which is an “en- hancement” of the quiver used to describe Hilbc (tot(OP1 (−n))).