How to use rigidifying in a sentence? Find typical usage patterns (collocations)/phrases/context for "rigidifying" and check conjugation/comparative form for "rigidifying". Mastering all the usages of "rigidifying" from sentence examples published by news publications.
Rigidifying on the cobblestones here, swinging her sword all swaggeringly there.
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This effect is repeated in white by the front headlamps. The front lights feature lens technology and a plexiglas edge to produce "C" shaped daytime driving lights with the help of LED headlamp technology. Translucent surfaces make the normally concealed technology visible. The light-grey tailgate is made completely from lightweight yet robust Polycarbonate that allows a view of the aluminium structure that makes up the rigidifying frame.
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With a suitable choice of the rigidifying data, the modified moduli problem will have a (fine) moduli space T, often described as a subscheme of a suitable Hilbert scheme or Quot scheme. The rigidifying data is moreover chosen so that it corresponds to a principal bundle with an algebraic structure group G. Thus one can move back from the rigidified problem to the original by taking quotient by the action of G, and the problem of constructing the moduli space becomes that of finding a scheme (or more general space) that is (in a suitably strong sense) the quotient T/G of T by the action of G. The last problem, in general, does not admit a solution; however, it is addressed by the groundbreaking geometric invariant theory (GIT), developed by David Mumford in 1965, which shows that under suitable conditions the quotient indeed exists. To see how this might work, consider the problem of parametrizing smooth curves of the genus g > 2. A smooth curve together with a complete linear system of degree d > 2g is equivalent to a closed one dimensional subscheme of the projective space Pd−g.
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In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased as rigidifying the geometry of X. In applications, a level structure is used in the construction of moduli spaces; a moduli space is often constructed as a quotient. The presence of automorphisms poses a difficulty to forming a quotient; thus introducing level structures helps overcome this difficulty. There is no single definition of a level structure; rather, depending on the space X, one introduces the notion of a level structure. The classic one is that on an elliptic curve (see #Example: an abelian scheme).
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The modern formulation of moduli problems and definition of moduli spaces in terms of the moduli functors (or more generally the categories fibred in groupoids), and spaces (almost) representing them, dates back to Grothendieck (1960/61), in which he described the general framework, approaches, and main problems using Teichmüller spaces in complex analytical geometry as an example. The talks, in particular, describe the general method of constructing moduli spaces by first rigidifying the moduli problem under consideration. More precisely, the existence of non-trivial automorphisms of the objects being classified makes it impossible to have a fine moduli space. However, it is often possible to consider a modified moduli problem of classifying the original objects together with additional data, chosen in such a way that the identity is the only automorphism respecting also the additional data.
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