TY - BOOK

T1 - The motivic zeta functions of Hilbert schemes of points on surfaces

AU - Pagano, Luigi

PY - 2022

Y1 - 2022

N2 - The main object of this thesis is the motivic zeta function for Calabi-Yau varieties defined over a non Archimedean valued field, focusing on Hilbert schemes of points on surfaces. We use the tools from logarithmic geometry for the construction of semistable models of the surfaces with trivial canonical sheaf. We exploit such construction in order to give a recipe for constructing weak Néron models of their Hilbert schemes of points and deduce from this a formula forcomputing their motivic zeta function. We use the formula developed in this way in order to prove that the Hilbert schemes of points have the monodromy property if their underlying surfaces have it.

AB - The main object of this thesis is the motivic zeta function for Calabi-Yau varieties defined over a non Archimedean valued field, focusing on Hilbert schemes of points on surfaces. We use the tools from logarithmic geometry for the construction of semistable models of the surfaces with trivial canonical sheaf. We exploit such construction in order to give a recipe for constructing weak Néron models of their Hilbert schemes of points and deduce from this a formula forcomputing their motivic zeta function. We use the formula developed in this way in order to prove that the Hilbert schemes of points have the monodromy property if their underlying surfaces have it.

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99124146972305763

M3 - Ph.D. thesis

BT - The motivic zeta functions of Hilbert schemes of points on surfaces

PB - Department of Mathematical Sciences, Faculty of Science, University of Copenhagen

ER -