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Extension of pluricanonical forms in positive and mixed characteristics
October 27, 2023 @ 12:00 pm - 1:00 pm
Member Seminar
Speaker: Iacopo Brivio (CMSA)
Title: Extension of pluricanonical forms in positive and mixed characteristics
Abstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms, i.e. global sections of $(\Omega^{\dim X}_X)^{\otimes m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring.