In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the projectivized tangent space at that point. The metaphor is that of zooming in on a photograph to enlarge part of the picture, rather than referring to an explosion. Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup. The weak factorization theorem says that every birational map can be factored as a composition of particularly simple blowups. The Cremona group, the group of birational automorphisms of the plane, is generated by blowups. Besides their importance in describing birational transformations, blowups are also an important way of constructing new spaces. For instance, most procedures for resolution of singularities proceed by blowing up singularities until they become smooth. A consequence of this is that blowups can be used to resolve the singularities of birational maps. Classically, blowups were defined extrinsically, by first defining the blowup on spaces such as projective space using an explicit construction in coordinates and then defining blowups on other spaces in terms of an embedding. This is reflected in some of the terminology, such as the classical term monoidal transformation. Contemporary algebraic geometry treats blowing up as an intrinsic operation on an algebraic variety. From this perspective, a blowup is the universal (in the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic transformation, dilatation, σ-process, or Hopf map. (Wikipedia).
What happened during the Big Bang?
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From playlist Science Unplugged: Cosmology
How To (Safely) Demolish A Building
When demolition companies “blow up” a skyscraper, they’re actually imploding the structure. So how do they collapse a building without destroying everything around it? Learn more at HowStuffWorks.com: http://science.howstuffworks.com/engineering/structural/building-implosion.htm Share on
From playlist Wackiest Comment Threads
What Happens if a Supervolcano Blows Up?
Go ‘beyond the nutshell’ at https://brilliant.org/nutshell by diving deeper into these topics and more with 20% off an annual subscription! This video was sponsored by Brilliant. Thanks a lot for the support! Sources & further reading: https://sites.google.com/view/sources-supervolcanoes/
From playlist The Existential Crisis Playlist
Watch the explosive demise of a weather balloon
What happens when a weather balloon climbs too high? Learn more: http://www.sciencemag.org/news/2017/03/watch-explosive-demise-weather-balloon
From playlist Materials and technology
Airbag Simulation | Literally Blowing Stuff Up in Blender
I was reading a paper about airbag deployment simulation in LS-DYNA the other day and thought, wouldn't it be cool to do this in Blender and to blow up Suzanne (the monkey) literally and inflating it like a balloon? Paper: https://goo.gl/22EyDC
From playlist Destruction Physics Demos
Now You Know: Bursting Balloons
When you stick a needle in a balloon, the rubber tears—the balloon pops. But high-speed video reveals the details, and there are some surprises to be had. How does the rubber unzip as it tears? It’s different for a round balloon and a longer balloon-animal balloon. And if the balloon is fi
From playlist Now You Know
AWESOME Physics demonstrations. The collapsing can.
This is a fun introduction to atmospheric pressure.
From playlist PRESSURE
Yes. I make mistakes ... rarely. http://www.flippingphysics.com
From playlist Miscellaneous
algebraic geometry 35 More on blow ups
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It continues the discussion of blowing up in the previous video, with examples, of blowing up the real affine plane, blowing up an ideal, and regularizing a ration map fro
From playlist Algebraic geometry I: Varieties
Alessio Porretta: Viscous Hamilton-Jacobi equations in the superquadratic case
We discuss properties of the viscous Hamilton-Jacobi equation $$\begin{cases}u_{t}-\Delta u=|D u|^{p} & \text { in }(0, \infty) \times \Omega, \\ u=0 & \text { in }(0, \infty) \times \partial \Omega, \\ u(0)=u_{0} & \text { in } \Omega,\end{cases}$$ in the super-quadratic case $p sup 2$. H
From playlist Partial Differential Equations
Complex surfaces 2: Minimal surfaces
This talk is part of a series about complex surfaces, and explains what minimal surfaces are. A minimial surfaces is one that cannot be obtained by blowing up a nonsingular surfaces at a point. We explain why every surface is birational to a minimal nonsingular projective surface. We disc
From playlist Algebraic geometry: extra topics
Jaroslaw Wlodarczyk: Functorial desingularization by torus actions
HYBRID EVENT Recorded during the meeting "Faces of Singularity Theory " the November 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovis
From playlist Algebraic and Complex Geometry
algebraic geometry 34 Blowing up a point
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers blowing up a point of affine space, and gives some examples of using this to resolve singularities of plane curves.
From playlist Algebraic geometry I: Varieties
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture III
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Schemes 45: Blowing up schemes
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we discuss the operation of blowing up a scheme along a sheaf of ideals. This can be used to make ideals invertible, and to eliminate points o
From playlist Algebraic geometry II: Schemes
IGA - Lars Sektnan Extremal Kähler metrics on blowups
Abstract: Extremal Kähler metrics were introduced by Calabi in the 80’s as a type of canonical Kähler metric on a Kähler manifold, and are a generalisation of constant scalar curvature Kähler metrics in the case when the manifold admits automorphisms. A natural question is when the blowup
From playlist Informal Geometric Analysis Seminar
Schemes 26: Abstract and projective varieties
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We discuss the relation between abstract, projective, and complete varieties, and given an example found by Hironaka of a complete variety that is not projecti
From playlist Algebraic geometry II: Schemes
What to do with all those old PCBs from stuff you've taken apart...
From playlist Projects & Installations
Abstraction - Seminar 2 - Resolution I, blowing up
This seminar series is on the relations among Natural Abstraction, Renormalisation and Resolution. This week Daniel Murfet gives an introduction to blowing up an affine algebraic variety at a point. The webpage for this seminar is https://metauni.org/abstraction/ You can join this semina
From playlist Abstraction