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Relevant bibliographies by topics / Log Fano varieties

Academic literature on the topic 'Log Fano varieties'

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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Journal articles on the topic "Log Fano varieties"

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Cheltsov, Ivan A., and Yanir A. Rubinstein. "Asymptotically log Fano varieties." Advances in Mathematics 285 (November 2015): 1241–300. http://dx.doi.org/10.1016/j.aim.2015.08.001.

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Fujita, Kento. "Simple normal crossing Fano varieties and log Fano manifolds." Nagoya Mathematical Journal 214 (June 2014): 95–123. http://dx.doi.org/10.1215/00277630-2430136.

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AbstractA projective log variety (X, D) is called a log Fano manifold if X is smooth and if D is a reduced simple normal crossing divisor on Χ with − (KΧ + D) ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are classified in this article when the log Fano index r of (X, D) satisfies either r ≥ n/2 with ρ(X) ≥ 2 or r ≥ n − 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

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Fujita, Kento. "Simple normal crossing Fano varieties and log Fano manifolds." Nagoya Mathematical Journal 214 (June 2014): 95–123. http://dx.doi.org/10.1017/s0027763000010862.

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AbstractA projective log variety (X, D) is called alog Fano manifoldifXis smooth and ifDis a reduced simple normal crossing divisor onΧwith − (KΧ+D) ample. Then-dimensional log Fano manifolds (X, D) with nonzeroDare classified in this article when the log Fano indexrof (X, D) satisfies eitherr≥n/2withρ(X) ≥ 2 orr≥n− 2. This result is a partial generalization of the classification of logarithmic Fano 3-folds by Maeda.

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Fujita, Kento. "On log K-stability for asymptotically log Fano varieties." Annales de la faculté des sciences de Toulouse Mathématiques 25, no. 5 (2016): 1013–24. http://dx.doi.org/10.5802/afst.1520.

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Karzhemanov, I. V. "Semiampleness theorem for weak log Fano varieties." Sbornik: Mathematics 197, no. 10 (October 31, 2006): 1459–65. http://dx.doi.org/10.1070/sm2006v197n10abeh003807.

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Schwede, Karl, and Karen E. Smith. "Globally F-regular and log Fano varieties." Advances in Mathematics 224, no. 3 (June 2010): 863–94. http://dx.doi.org/10.1016/j.aim.2009.12.020.

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Anderson, Dave, and Alan Stapledon. "Schubert varieties are log Fano over the integers." Proceedings of the American Mathematical Society 142, no. 2 (November 4, 2013): 409–11. http://dx.doi.org/10.1090/s0002-9939-2013-11779-x.

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Hassett, Brendan, and Yuri Tschinkel. "Log Fano varieties over function fields of curves." Inventiones mathematicae 173, no. 1 (February 5, 2008): 7–21. http://dx.doi.org/10.1007/s00222-008-0113-2.

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Okumura, Katsuhiko. "SNC Log Symplectic Structures on Fano Products." Canadian Mathematical Bulletin 63, no. 4 (February 24, 2020): 891–900. http://dx.doi.org/10.4153/s0008439520000120.

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AbstractThis paper classifies Poisson structures with the reduced simple normal crossing divisor on a product of Fano varieties of Picard number 1. The characterization of even-dimensional projective spaces from the viewpoint of Poisson structures is given by Lima and Pereira. In this paper, we generalize the characterization of projective spaces to any dimension.

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Lohmann, Daniel. "Families of canonically polarized manifolds over log Fano varieties." Compositio Mathematica 149, no. 6 (March 26, 2013): 1019–40. http://dx.doi.org/10.1112/s0010437x1200053x.

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AbstractLet $(X,D)$ be a dlt pair, where $X$ is a normal projective variety. We show that any smooth family of canonically polarized varieties over $X\setminus \,{\rm Supp}\lfloor D \rfloor $ is isotrivial if the divisor $-(K_X+D)$ is ample. This result extends results of Viehweg–Zuo and Kebekus–Kovács. To prove this result we show that any extremal ray of the moving cone is generated by a family of curves, and these curves are contracted after a certain run of the minimal model program. In the log Fano case, this generalizes a theorem by Araujo from the klt to the dlt case. In order to run the minimal model program, we have to switch to a $\mathbb Q$-factorialization of $X$. As $\mathbb Q$-factorializations are generally not unique, we use flops to pass from one $\mathbb Q$-factorialization to another, proving the existence of a $\mathbb Q$-factorialization suitable for our purposes.

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Dissertations / Theses on the topic "Log Fano varieties"

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Lohmann, Daniel [Verfasser], and Stefan [Akademischer Betreuer] Kebekus. "Families of canonically polarized manifolds over log Fano varieties = Familien kanonisch polarisierter Mannigfaltigkeiten über log Fano Varietäten." Freiburg : Universität, 2011. http://d-nb.info/1123463352/34.

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Heuberger, Liana. "Deux points de vue sur les variétés de Fano : géométrie du diviseur anticanonique et classification des surfaces à singularités 1/3(1,1)." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066129/document.

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Cette thèse concerne l'étude des variétés de Fano, qui sont des objets centraux de la classification des variétés algébriques. La première question abordée concerne les variétés de Fano lisses de dimension quatre. On cherche a étudier les potentielles singularités d'un diviseur anticanonique de sorte qu'on puisse les écrire sous une forme locale explicite. En tant qu'étape intermédiaire, on démontre aussi que ces points sont au plus des singularités terminales, c'est-à-dire les singularités les plus proches du cas lisse du point de vue de la géométrie birationnelle. On montre ensuite que ce dernier résultat se généralise en dimension arbitraire en admettant une conjecture de non-annulation de Kawamata.De façon complémentaire, on s¿intéresse à des variétés de Fano de dimension plus petite, mais admettant des singularités. Il s¿agit des surfaces de del Pezzo ayant des singularités de type 1/3(1,1). Ceci est l'exemple le plus simple de singularité rigide, c'est-à-dire qui reste inchangée à une déformation Q-Gorenstein près. On classifie entièrement ces objets en trouvant 29 familles. On obtient ainsi un tableau contenant des modèles de ces surfaces, qui pour la plupart sont des intersections complètes dans des variétés toriques. Ce travail s'inscrit dans un contexte plus large, qui a pour cible de calculer leur cohomologie quantique pour ensuite vérifier si deux conjectures en symmetrie miroir
This thesis concerns Fano varieties, which are central objects within the classification of algebraic varieties.The first problem we discuss involves smooth Fano varieties of dimension four. We study the potential singularities of an anticanonical divisor and determine their explicit local expression. As an intermediate step, we show that they are terminal points, that is the singularities which are closest to the smooth case from the point of view of birational geometry. We then show that the latter result generalizes in arbitrary dimension if we suppose that a nonvanishing conjecture of Kawamata holds.The second approach is to examine Fano varieties of smaller dimensions which admit singularities. The objects we consider are log del Pezzo surfaces with 1/3(1,1) points. This is the simplest example of a rigid singularity, that is it remains unchanged under Q-Gorenstein deformations. We give a complete classification of these surfaces, finding 29 families. We also provide a table describing almost all of them as complete intersections in toric varieties. This work belongs to an overarching project that aims at studying mirror symmetry for del Pezzo surfaces with cyclic quotient singularities

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Books on the topic "Log Fano varieties"

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Designs, High Planners. Tea Tasting Log Book, Cozying up with Tea and Great Reads: Tea Lovers Tasting Notebook Journal to Record, Rate and Review All the Tea Types, Varieties You Drink Checklists, Gift for Lovers, Fans, Addiction. Independently Published, 2021.

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Book chapters on the topic "Log Fano varieties"

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Jankowicz-Cieslak, Joanna, Ivan L. Ingelbrecht, and Bradley J. Till. "Mutation Detection in Gamma-Irradiated Banana Using Low Coverage Copy Number Variation." In Efficient Screening Techniques to Identify Mutants with TR4 Resistance in Banana, 113–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-64915-2_8.

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AbstractMutagenesis of in vitro propagated bananas is an efficient method to introduce novel alleles and broaden genetic diversity. The FAO/IAEA Plant Breeding and Genetics Laboratory previously established efficient methods for mutation induction of in vitro shoot tips in banana using physical and chemical mutagens as well as methods for the efficient discovery of ethyl methanesulphonate (EMS) induced single nucleotide mutations in targeted genes. Officially released mutant banana varieties have been created using gamma rays, a mutagen that can produce large genomic changes such as insertions and deletions (InDels). Such dosage mutations may be particularly important for generating observable phenotypes in polyploids such as banana. Here, we describe a Next Generation Sequencing (NGS) approach in Cavendish (AAA) bananas to identify large genomic InDels. The method is based on low coverage whole genome sequencing (LC-WGS) using an Illumina short-read sequencing platform. We provide details for sonication-mediated library preparation and the installation and use of freely available computer software to identify copy number variation in Cavendish banana. Alternative DNA library construction procedures and bioinformatics tools are briefly described. Example data is provided for the mutant variety Novaria and cv Grande Naine (AAA), but the methodology can be equally applied for triploid bananas with mixed genomes (A and B) and is useful for the characterization of putative Fusarium Wilt TR4 resistant mutant lines described elsewhere in this protocol book.

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