Birational geometry | Vector bundles
In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L. This is 1 less than the dimension of the section ring of L The Iitaka dimension of L is always less than or equal to the dimension of X. If L is not effective, then its Iitaka dimension is usually defined to be or simply said to be negative (some early references define it to be −1). The Iitaka dimension of L is sometimes called L-dimension, while the dimension of a divisor D is called D-dimension. The Iitaka dimension was introduced by Shigeru Iitaka . (Wikipedia).
Junyan Cao: Kodaira dimension of algebraic fiber spaces over abelian varieties or projective...
Abstract: Let f:X→Y be a fibration between two projective manifolds. The Iitaka’s conjecture predicts that the Kodaira dimension of X is larger than the sum of the Kodaira dimension of X and the Kodaira dimension of the generic fiber. We explain a proof of the Iitaka conjecture for algebra
From playlist Algebraic and Complex Geometry
Hyperbolicity and Fundamental groups (Lecture 2) by Yohan Brunebarbe
PROGRAM : TOPICS IN BIRATIONAL GEOMETRY ORGANIZERS : Indranil Biswas and Mahan Mj DATE : 27 January 2020 to 31 January 2020 VENUE : Madhava Lecture Hall, ICTS Bangalore Birational geometry is one of the current research trends in fields of Algebraic Geometry and Analytic Geometry. It ca
From playlist Topics In Birational Geometry
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals
From playlist Dimensions Arabe/Arabic / العربية
From playlist Dimensions Arabe/Arabic / العربية
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
From playlist Dimensions Arabe/Arabic / العربية
From playlist Dimensions Japanese / 日本語
From playlist Dimensions Arabe/Arabic / العربية
From playlist Dimensions Arabe/Arabic / العربية
From playlist Dimensions Arabe/Arabic / العربية
Commutative algebra 53: Dimension Introductory survey
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:
From playlist Commutative algebra
Kenneth Falconer: Intermediate dimensions, capacities and projections
The talk will review recent work on intermediate dimensions which interpolate between Hausdorff and box dimensions. We relate these dimensions to capacities which leading to ‘Marstrand-type’ theorems on the intermediate dimensions of projections of a set in $\mathbb{R}^{n}$ onto almost all
From playlist Analysis and its Applications
algebraic geometry 14 Dimension
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.
From playlist Algebraic geometry I: Varieties
Juan M. Maldacena - Are there Extra Dimensions?
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Extra dimensions—beyond length, width, height—seem like the stuff of science fiction. What would extra dimensions be like? Is time the fourth dimension? Does string theory require ten or eleven dimensions? Cou
From playlist Exploring the Multiverse - Closer To Truth - Core Topic
Dave Richeson - A Romance of Many (and Fractional) Dimensions - CoM Oct 2021
Dimension seems like an intuitive idea. We are all familiar with zero-dimensional points, one-dimensional curves, two-dimensional surfaces, and three-dimensional solids. Yet dimension is a slippery idea that took mathematicians many years to understand. We will discuss the history of dimen
From playlist Celebration of Mind 2021
Are there Extra Dimensions? | Episode 406 | Closer To Truth
Extra dimensions -beyond length, width, height- seem the stuff of science fiction. What would extra dimensions be like? Is time the fourth dimension? Could deep reality be so strange? And, anyway, why would we care? Featuring interviews with Lawrence Krauss, Michio Kaku, David Gross, Nima
From playlist Closer To Truth | Season 4
Benjamin Schweinhart (4/3/18): Persistent homology and the upper box dimension
We prove the first results relating persistent homology to a classically defined fractal dimension. Several previous studies have demonstrated an empirical relationship between persistent homology and fractal dimension; our results are the first rigorous analogue of those comparisons. Spe
From playlist AATRN 2018
Commutative algebra 55: Dimension of local rings
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give 4 definitions of the dimension of a Noetherian local ring: Brouwer-Menger-Urysohn dimension, Krull dimension, degree o
From playlist Commutative algebra
From playlist Dimensions Arabe/Arabic / العربية