Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension
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In this article, the authors propose a method to solve the problem of the lack of an EKG-based EKF-based sensor network for medical data collection, which is called EPFL-ARTICLE-231100.Abstract:
Reference EPFL-ARTICLE-231100doi:10.1090/jams/871 URL: http://dx.doi.org/10.1090/jams/871 Record created on 2017-09-19, modified on 2017-10-02read more
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K-stability of Fano varieties: an algebro-geometric approach
TL;DR: A survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach is given in this article, where the authors also give a survey of recent progress in this area.
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Singularities of General Fibers and the LMMP
Zsolt Patakfalvi,Joe Waldron +1 more
TL;DR: In this paper, the authors use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change, and show that it is linearly equivalent to a divisors with positive integer coefficients divisible by $p-1.
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Openness of uniform K-stability in families of $\mathbb{Q}$-Fano varieties
Harold Blum,Yuchen Liu +1 more
TL;DR: In this article, it was shown that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties and that the stability threshold is lower semicontinuous in families.
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Positivity of the CM line bundle for families of K-stable klt Fano varieties
Giulio Codogni,Zsolt Patakfalvi +1 more
TL;DR: In this article, the authors prove the ampleness of the Chow-Mumford line bundle for families with K-semi-stable/K-polystable fibers. But they do not consider the case of k-poly-stable klt Fano varieties.
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Geometry and moduli of polarised varieties
TL;DR: In this article, the authors investigated the geometry of projective varieties polarised by ample and more generally nef and big Weil divisors, and showed the boundedness of polarised Calabi-Yau pairs under some natural conditions.
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Book
Compact Complex Surfaces
TL;DR: In this article, the authors describe the topology and algebraic properties of complex surfaces, including the following properties: 1. The Projective Plane, 2. The Jacobian Fibration, 3. Hodge Theory on Surfaces, 4. Inequahties for Hodge Numbers, 5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch Theorem.
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The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
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Birational Geometry of Algebraic Varieties
János Kollár,Shigefumi Mori +1 more
TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
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Existence of minimal models for varieties of log general type
TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.