scholarly journals BOUNDING VOLUMES OF SINGULAR FANO THREEFOLDS

2016 ◽  
Vol 224 (1) ◽  
pp. 37-73 ◽  
Author(s):  
CHING-JUI LAI
Keyword(s):  
Upper Bound ◽  
Main Idea ◽  
Fano Varieties ◽  
Fano Threefolds ◽  
Bounding Volumes

Let $(X,\unicode[STIX]{x1D6E5})$ be an $n$-dimensional $\unicode[STIX]{x1D716}$-klt log $\mathbb{Q}$-Fano pair. We give an upper bound for the volume $\text{Vol}(X,\unicode[STIX]{x1D6E5})=(-(K_{X}+\unicode[STIX]{x1D6E5}))^{n}$ when $n=2$, or $n=3$ and $X$ is $\mathbb{Q}$-factorial of $\unicode[STIX]{x1D70C}(X)=1$. This bound is essentially sharp for $n=2$. The main idea is to analyze the covering families of tigers constructed in J. McKernan (Boundedness of log terminal fano pairs of bounded index, preprint, 2002, arXiv:0205214). Existence of an upper bound for volumes is related to the Borisov–Alexeev–Borisov Conjecture, which asserts boundedness of the set of $\unicode[STIX]{x1D716}$-klt log $\mathbb{Q}$-Fano varieties of a given dimension $n$.

scholarly journals Nonrational Weighted Hypersurfaces

2009 ◽  
Vol 194 ◽  
pp. 1-32 ◽  
Author(s):  
Takuzo Okada
Keyword(s):  
Arbitrary Dimension ◽  
Fano Varieties ◽  
Fano Threefolds ◽  
Alternate Proof ◽  
Quotient Singularities

AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].

scholarly journals Canonical Toric Fano Threefolds

2010 ◽  
Vol 62 (6) ◽  
pp. 1293-1309 ◽  
Author(s):  
Alexander M. Kasprzyk
Keyword(s):  
Fano Varieties ◽  
Fano Threefolds ◽  
Inductive Approach ◽  
Canonical Singularities ◽  
Toric Fano Varieties

AbstractAn inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.

Making the Error-Controlling Algorithm of Observable Operator Models Constructive

2009 ◽  
Vol 21 (12) ◽  
pp. 3460-3486
Author(s):  
Ming-Jie Zhao ◽  
Herbert Jaeger ◽  
Michael Thon
Keyword(s):  
Upper Bound ◽  
Markov Models ◽  
Learning Algorithms ◽  
Main Idea ◽  
Statistical Efficiency ◽  
Modeling Error ◽  
Finite Dimensional ◽  
Learning Speed ◽  
Modeling Accuracy ◽  
Order Of Magnitude

Observable operator models (OOMs) are a class of models for stochastic processes that properly subsumes the class that can be modeled by finite-dimensional hidden Markov models (HMMs). One of the main advantages of OOMs over HMMs is that they admit asymptotically correct learning algorithms. A series of learning algorithms has been developed, with increasing computational and statistical efficiency, whose recent culmination was the error-controlling (EC) algorithm developed by the first author. The EC algorithm is an iterative, asymptotically correct algorithm that yields (and minimizes) an assured upper bound on the modeling error. The run time is faster by at least one order of magnitude than EM-based HMM learning algorithms and yields significantly more accurate models than the latter. Here we present a significant improvement of the EC algorithm: the constructive error-controlling (CEC) algorithm. CEC inherits from EC the main idea of minimizing an upper bound on the modeling error but is constructive where EC needs iterations. As a consequence, we obtain further gains in learning speed without loss in modeling accuracy.

scholarly journals Balanced line bundles on Fano varieties

2018 ◽  
Vol 2018 (743) ◽  
pp. 91-131 ◽  
Author(s):  
Brian Lehmann ◽  
Sho Tanimoto ◽  
Yuri Tschinkel
Keyword(s):  
Minimal Model ◽  
Line Bundles ◽  
Fano Varieties ◽  
Model Program ◽  
Minimal Model Program ◽  
Fano Threefolds ◽  
Arithmetic Properties ◽  
Geometric Invariants

Abstract A conjecture of Batyrev and Manin relates arithmetic properties of varieties with ample anticanonical class to geometric invariants. We analyze the geometry underlying these invariants using the Minimal Model Program and then apply our results to primitive Fano threefolds.

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

From Freezing to Investing: New Approaches to Monetary and Currency Policies

2008 ◽  
pp. 47-55
Author(s):  
A. Nekipelov ◽  
Yu. Goland
Keyword(s):  
Economic Policy ◽  
Property Rights ◽  
Main Idea ◽  
State Intervention ◽  
Economic Thought ◽  
Human Potential ◽  
Knowledge Based ◽  
Russian Economy ◽  
Knowledge Based Economy

The appeals to minimize state intervention in the Russian economy are counterproductive. However the excessive involvement of the state is fraught with the threat of building nomenclature capitalism. That is the main idea of the series of articles by prominent representatives of Russian economic thought who formulate their position on key elements of the long-term strategy of Russia’s development. The articles deal with such important issues as Russia’s economic policy, transition to knowledge-based economy, basic directions of monetary and structural policies, strengthening of property rights, development of human potential, foreign economic priorities of our state.

PENGARUH MODEL PEMBELAJARAN COOPERATIVE INTEGRATED READING AND COMPOSITION (CIRC) TERHADAP KEMAMPUAN MENENTUKAN IDE POKOK PARAGRAF SISWA KELAS V SD NEGERI 003 PULAU KOPUNG KECAMATAN SENTAJO RAYA KABUPATEN KUANTAN SINGINGI

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Yuwanda Megri Santika ◽  
Otang Kurniaman ◽  
Zariul Antosa
Keyword(s):  
Main Idea ◽  
Learning Model ◽  
Communication Process ◽  
Fifth Grade ◽  
Control Group ◽  
Control Group Design ◽  
Group Design ◽  
Fifth Grade Students ◽  
Quasi Experimental ◽  
Main Ideas

Reading is one of the important aspects in the communication process. Reading can make someone better understand the contents of the reading. In learning to make it easier for students to understand the contents of the reading it will be easier if it begins with the ability to determine the main ideas of the paragraph. Based on this, the researcher conducted a study by applying the Cooperative Integrated Reading and Composition (CIRC) learning model to the ability to determine the main idea of the paragraph at the fifth grade students of SD 003 Pulau Kopung. This study aims to determine the effect of the CIRC learning model on the ability to determine the main ideas of paragraphs of fifth grade students of SD Negeri 003 Pulau Kopung. This research method is a quasi- experimental Nonequivalent Control Group Design. This research was conducted in two classes, the VA class as the control class and VB class as the experimental class with 22 students in each class. The results of the study showed that the CIRC learning model influenced the ability to determine paragraph main ideas with the results of calculations derived from the gain index, the experimental class using the CIRC learning model got an increase in gain of 0.59 with the middle class and the control class with the normal learning model got an increase of 0.31 with medium class.

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