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Let $X$ be a compact Kähler manifold. The so-called Kodaira problem asks whether $X$ has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Voisin which answer the Kodaira problem in the negative. In this talk, we will focus on threefolds, as well as compact Kähler manifolds of algebraic dimension $a(X) = dim(X) -1$. We will explain our positive solution to the Kodaira problem for these manifolds.[-]
Let $X$ be a compact Kähler manifold. The so-called Kodaira problem asks whether $X$ has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Voisin which answer the Kodaira problem in the negative. In this talk, we will focus on threefolds, as well as compact Kähler manifolds of algebraic dimension $a(X) = ...[+]

32J17 ; 32J27 ; 32J25 ; 32G05 ; 14D06 ; 14E30

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A universal motivic invariant of birational maps - Lin, Hsueh-Yung (Author of the conference) | CIRM H

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(Joint work in progress with E. Shinder).We will introduce Grothendieck groups of pairs and explain their relations with the motivic invariants of birational maps. In particular, our construction provides a motivic perspective on the invariants of birational maps introduced by Genevois,Lonjou, and Urech based on median geometry.

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