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On the cone of divisors of Calabi-Yau fiber spaces

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TLDR
In this paper, the authors prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.
Abstract
We prove some version of Morrison's conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.

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Lectures on K3 Surfaces

TL;DR: Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular and each chapter ends with questions and open problems.
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A survey of Torelli and monodromy results for holomorphic-symplectic varieties

TL;DR: A survey of recent results about the Torelli question for holomorphicsymplectic varieties can be found in this article, where the main topics are a Hodge theoretic Hodge theorem and a discussion of the moduli spaces of polarized holomorphic symplectic varieties as monodromy quotients of period domains of type IV.
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Extension theorems, non-vanishing and the existence of good minimal models

TL;DR: In this paper, an extension theorem for effective purely log-terminal pairs (X, S+B) of non-negative Kodaira dimension is presented. But the main new ingredient is a refinement of the Ohsawa-Takegoshi L 2 extension theorem involving singular Hermitian metrics.
References
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Smooth Compactifications of Locally Symmetric Varieties

TL;DR: In this article, the authors present a universal method for the resolution of a class of singularities in algebraic geometry, which brings together ideas from algebraic geometrical, differential geometry, representation theory and number theory.