Motivic Integrals of Orbifolds

Student: Bhamidipati Deewang

Educational Programme: Mathematics (Master)

Year of Graduation: 2019

Given a K3 surface $X$ over $\ff_p$, we compute the Betti Numbers of its Hilbert Scheme of Points in terms of the Betti Number of its Symmetric Powers; and present a proof of an expression of the Poincar{\'e} Polynomial of its Hilbert Scheme of Points in terms of the Poincar{\'e} Polynomial of its Symmetric Powers, as given in \cite[2.2]{lgp}. This is achieved by computing an expression of a Non-Archimedean volume, with respect to a $K$: a Non-Archimedean local field of characteristic $p$, of the Hilbert Scheme of Points of an extension of $X$ over $K$.

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