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2021년 2월 17일 (수) 00:48 기준 최신판

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  1. Thus there arises the module of syzygies, the chain complex of syzygies, etc.[1]
  2. Syzygies appear in the definition of syzygetic ideals and the theory of regular algebras and regular sequences, cf.[1]
  3. Syzygies occur in tensors at rank 5, 7, 8, and all higher ranks, and play a role in restricting the number of independent isotropic tensors.[2]
  4. The syzygy module depends on the choice of a generating set, but it is unique up to the direct sum with a free module.[3]
  5. The module of trivial relations of an ideal is the submodule of the first syzygy module of the ideal that is generated by the trivial relations between the elements of a generating set of an ideal.[3]
  6. If the ring R is Noetherian, or, at least coherent, and if M is finitely generated, then the syzygy module is also finitely generated.[3]
  7. A fundamental property of syzygies modules is that there are "stably independent" on choices of generating sets for involved modules.[3]
  8. Hilbert's syzygy theorem is now considered to be an early result of homological algebra.[4]
  9. Part III contains the syzygy theorem (Theorem III), which is used in part IV to discuss the Hilbert polynomial.[4]
  10. Let n be the smallest integer, if any, such that the nth syzygy module of a module M is free or projective.[4]
  11. At Hilbert's time, there were no method available for computing syzygies.[4]
  12. Nowadays, syzygies and, more generally, free resolutions are powerful tools to relate the algebra and geometry of a projective variety.[5]
  13. It begins by explaining syzygies and their connection with the Hilbert function, and turns to describing various aspects of algebraic geometry … .[6]
  14. "This monograph is devoted to the geometric properties of a projective variety corresponding to the properties of its syzygies … .[6]
  15. “This very interesting book is the first textbook-level account of syzygies as they are used in algebraic geometry.[6]
  16. We introduce a weak order ideal property that suffices for establishing the Evans–Griffith Syzygy Theorem.[7]
  17. If k>0 then the syzygy module is computed from the resolution.[8]
  18. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study.[9]
  19. It illustrates the use of syzygies in many concrete geometric considerations, from interpolation to the study of canonical curves.[9]
  20. In this thesis we use the theory of syzygies to represent a surface implicitly by a matrix whose maximal-sized minors have the implicit equation of the surface as their greatest common divisor.[10]
  21. We show that a representation matrix can be constructed only using linear syzygies and we give a simple and efficient algorithm for its computation.[10]
  22. With a similar argument, we prove the semistability of a certain syzygy bundle on a general complete intersection of hypersurfaces of degree d in the projective space.[11]
  23. We then give an elementary proof of H. Brenner's criterion of stability for monomial syzygy bundles, avoiding the use of Klyachko's results on toric vector bundles.[11]
  24. We finally prove the existence of stable syzygy bundles defined by monomials of the same degree d, of any possible rank, for n at least 3.[11]
  25. We study derived invariance through syzygy complexes.[12]
  26. In particular, we prove that syzygy-finite algebras and Igusa--Todorov algebras are invariant under derived equivalences.[12]
  27. If we follow such an orbit there will be a later instant at which the three bodies become colinear: the instant of syzygy.[13]
  28. In this manner we can define a flow-induced “Poincare map” from brake initial conditions to syzygy configurations.[13]
  29. Appropriately viewed, this brake-to-syzygy map is a map between planar domains.[13]
  30. Syzygy has been used by over 16,000 students at 20 universities.[14]
  31. The Syzygy experiment has shown that using Jupyter in educational programs drives interest in using Jupyter for research (and vice versa).[14]
  32. The Syzygy project has demonstrated that it’s possible to deploy tools for interactive computation at a national scale rapidly and efficiently using an entirely open source technology stack.[14]
  33. Students, faculty and staff across Canada use Syzygy to access Jupyter through their browsers with their university single-sign-on credentials.[14]
  34. C.3 Syzygies and resolutions Syzygies Let be a quotient of and let be a submodule of .[15]
  35. Then the module of syzygies (or 1st syzygy module, module of relations) of , syz( ), is defined to be the kernel of the map .[15]
  36. The k-th syzygy module is defined inductively to be the module of syzygies of the -stsyzygy module.[15]
  37. Note, that the syzygy modules of depend on a choice of generators .[15]
  38. : I plan to sketch the proof of my joint work with R. Lazarsfeld on the gonality conjecture on the syzygies of algebraic curves of large degree.[16]
  39. This workshop, aimed at graduate students and young postdocs, will expose participants to some current research topics on Syzygies of Algebraic Varieties.[16]
  40. Our goal is to give a dynamical method for computing a finite basis for the syzygy module of finitely many multivariate Laurent polynomials with coefficients in a Dedekind ring .[17]
  41. More precisely, given nonzero polynomials , we will compute generating the syzygy module .[17]
  42. (1)Let be a monoid in and be the syzygy module of the vector whose elements are considered in .[17]
  43. Now, we can give a method for computing a set of generators for the syzygy module, , over the Laurent polynomial ring .[17]

소스

  1. ↑ 1.0 1.1 Encyclopedia of Mathematics
  2. ↑ Syzygy -- from Wolfram MathWorld
  3. ↑ 3.0 3.1 3.2 3.3 Linear relation
  4. ↑ 4.0 4.1 4.2 4.3 Hilbert's syzygy theorem
  5. ↑ What is ... a syzygy?
  6. ↑ 6.0 6.1 6.2 The Geometry of Syzygies - A Second Course in Algebraic Geometry and Commutative Algebra
  7. ↑ Syzygy Theorems via comparison of order ideals on a hypersurface
  8. ↑ syzygyModule -- Produces the k-th syzygy module (k \in ZZ)
  9. ↑ 9.0 9.1 The Geometry of Syzygies
  10. ↑ 10.0 10.1 Implicitization of rational algebraic surfaces with syzygy-based methods
  11. ↑ 11.0 11.1 11.2 ON THE STABILITY OF SYZYGY BUNDLES
  12. ↑ 12.0 12.1 Derived invariance by syzygy complexes
  13. ↑ 13.0 13.1 13.2 From Brake to Syzygy in the Three-Body Problem
  14. ↑ 14.0 14.1 14.2 14.3 National Scale Interactive Computing
  15. ↑ 15.0 15.1 15.2 15.3 Singular Manual: Syzygies and resolutions
  16. ↑ 16.0 16.1 UIC RTG Syzygy Workshop
  17. ↑ 17.0 17.1 17.2 17.3 On Syzygy Modules over Laurent Polynomial Rings

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