Articles de revues : « Geometry, Algebraic »

1

Hacon, Christopher, Daniel Huybrechts, Yujiro Kawamata et Bernd Siebert. « Algebraic Geometry ». Oberwolfach Reports 12, n^o 1 (2015) : 783–836. http://dx.doi.org/10.4171/owr/2015/15.

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Tyurin, N. A. « Algebraic Lagrangian geometry : three geometric observations ». Izvestiya : Mathematics 69, n^o 1 (28 février 2005) : 177–90. http://dx.doi.org/10.1070/im2005v069n01abeh000527.

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Voisin, Claire. « Algebraic Geometry versus Kähler geometry ». Milan Journal of Mathematics 78, n^o 1 (17 mars 2010) : 85–116. http://dx.doi.org/10.1007/s00032-010-0113-8.

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PLOTKIN, BORIS. « SOME RESULTS AND PROBLEMS RELATED TO UNIVERSAL ALGEBRAIC GEOMETRY ». International Journal of Algebra and Computation 17, n^o 05n06 (août 2007) : 1133–64. http://dx.doi.org/10.1142/s0218196707003986.

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In universal algebraic geometry (UAG), some primary notions of classical algebraic geometry are applied to an arbitrary variety of algebras Θ and an arbitrary algebra H ∈ Θ. We consider an algebraic geometry in Θ over the distinguished algebra H and we also analyze H from the point of view of its geometric properties. This insight leads to a system of new notions and stimulates a number of new problems. They are new with respect to algebra, algebraic geometry and even with respect to the classical algebraic geometry. In our approach, there are two main aspects: the first one is a study of the algebra H and its geometric properties, while the second is focused on studying algebraic sets and algebraic varieties over a "good", particular algebra H. Considering the subject from the second standpoint, the main goal is to get forward as far as possible in a classification of algebraic sets over the given H. The first approach does not require such a classification which is itself an independent and extremely difficult task. We also consider some geometric relations between different H1 and H2 in Θ. The present paper should be viewed as a brief review of what has been done in universal algebraic geometry. We also give a list of unsolved problems for future work.

5

Toën, Bertrand. « Derived algebraic geometry ». EMS Surveys in Mathematical Sciences 1, n^o 2 (2014) : 153–245. http://dx.doi.org/10.4171/emss/4.

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Debarre, Olivier, David Eisenbud, Gavril Farkas et Ravi Vakil. « Classical Algebraic Geometry ». Oberwolfach Reports 18, n^o 2 (24 août 2022) : 1519–77. http://dx.doi.org/10.4171/owr/2021/29.

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Darke, Ian, et M. Reid. « Undergraduate Algebraic Geometry ». Mathematical Gazette 73, n^o 466 (décembre 1989) : 351. http://dx.doi.org/10.2307/3619332.

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Debarre, Olivier, David Eisenbud, Frank-Olaf Schreyer et Ravi Vakil. « Classical Algebraic Geometry ». Oberwolfach Reports 9, n^o 2 (2012) : 1845–93. http://dx.doi.org/10.4171/owr/2012/30.

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Catanese, Fabrizio, Christopher Hacon, Yujiro Kawamata et Bernd Siebert. « Complex Algebraic Geometry ». Oberwolfach Reports 10, n^o 2 (2013) : 1563–627. http://dx.doi.org/10.4171/owr/2013/27.

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Debarre, Olivier, David Eisenbud, Gavril Farkas et Ravi Vakil. « Classical Algebraic Geometry ». Oberwolfach Reports 11, n^o 3 (2014) : 1695–745. http://dx.doi.org/10.4171/owr/2014/31.

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Debarre, Olivier, David Eisenbud, Gavril Farkas et Ravi Vakil. « Classical Algebraic Geometry ». Oberwolfach Reports 13, n^o 2 (2016) : 1635–82. http://dx.doi.org/10.4171/owr/2016/29.

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Debarre, Olivier, David Eisenbud, Gavril Farkas et Ravi Vakil. « Classical Algebraic Geometry ». Oberwolfach Reports 15, n^o 3 (26 août 2019) : 1983–2031. http://dx.doi.org/10.4171/owr/2018/33.

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Leykin, Anton. « Numerical algebraic geometry ». Journal of Software for Algebra and Geometry 3, n^o 1 (2011) : 5–10. http://dx.doi.org/10.2140/jsag.2011.3.5.

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ODAGIRI, Shinsuke. « Tropical algebraic geometry ». Hokkaido Mathematical Journal 38, n^o 4 (novembre 2009) : 771–95. http://dx.doi.org/10.14492/hokmj/1258554243.

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Blake, I., C. Heegard, T. Hoholdt et V. Wei. « Algebraic-geometry codes ». IEEE Transactions on Information Theory 44, n^o 6 (1998) : 2596–618. http://dx.doi.org/10.1109/18.720550.

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Shaska, T. « Computational algebraic geometry ». Journal of Symbolic Computation 57 (octobre 2013) : 1–2. http://dx.doi.org/10.1016/j.jsc.2013.05.001.

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Nishimura, Hirokazu. « Empirical algebraic geometry ». International Journal of Theoretical Physics 34, n^o 3 (mars 1995) : 305–21. http://dx.doi.org/10.1007/bf00671594.

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Joyce, D. « Hypercomplex Algebraic Geometry ». Quarterly Journal of Mathematics 49, n^o 2 (1 juin 1998) : 129–62. http://dx.doi.org/10.1093/qmathj/49.2.129.

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Daniyarova, E. Yu, A. G. Myasnikov et V. N. Remeslennikov. « Universal algebraic geometry ». Doklady Mathematics 84, n^o 1 (août 2011) : 545–47. http://dx.doi.org/10.1134/s1064562411050073.

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Verschelde, J. « Basic algebraic geometry ». Journal of Computational and Applied Mathematics 66, n^o 1-2 (janvier 1996) : N3—N4. http://dx.doi.org/10.1016/0377-0427(96)80471-7.

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Wampler, Charles W., et Andrew J. Sommese. « Numerical algebraic geometry and algebraic kinematics ». Acta Numerica 20 (28 avril 2011) : 469–567. http://dx.doi.org/10.1017/s0962492911000067.

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In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

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Bambozzi, Federico, et Oren Ben-Bassat. « Dagger geometry as Banach algebraic geometry ». Journal of Number Theory 162 (mai 2016) : 391–462. http://dx.doi.org/10.1016/j.jnt.2015.10.023.

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Sederberg, Thomas, et Ronald Goldman. « Algebraic Geometry for Computer-Aided Geometric Design ». IEEE Computer Graphics and Applications 6, n^o 6 (1986) : 52–59. http://dx.doi.org/10.1109/mcg.1986.276742.

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Daniyarova, E. Yu, A. G. Myasnikov et V. N. Remeslennikov. « Algebraic geometry over algebraic structures. II. Foundations ». Journal of Mathematical Sciences 185, n^o 3 (1 août 2012) : 389–416. http://dx.doi.org/10.1007/s10958-012-0923-z.

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Chandrashekara A C. « System Hypothesis Implications of Algebraic Geometry ». international journal of engineering technology and management sciences 7, n^o 1 (28 février 2023) : 105–8. http://dx.doi.org/10.46647/ijetms.2023.v07i01.018.

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Certain pole-placement concepts, such as an enhanced form of pole location with output response, are proven using fundamental algebraic geometry equations. Illustrations that highlight the algebra-geometric equations drawbacks and its possible application to systems analysis are shown. This study and ones that may come after it may help to make the potent theorems of current algebraic geometry comprehensible and useful for solving technical hurdles.

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BELLUCE, LAWRENCE P., ANTONIO DI NOLA et GIACOMO LENZI. « ALGEBRAIC GEOMETRY FOR MV-ALGEBRAS ». Journal of Symbolic Logic 79, n^o 4 (décembre 2014) : 1061–91. http://dx.doi.org/10.1017/jsl.2014.53.

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AbstractIn this paper we try to apply universal algebraic geometry to MV algebras, that is, we study “MV algebraic sets” given by zeros of MV polynomials, and their “coordinate MV algebras”. We also relate algebraic and geometric objects with theories and models taken in Łukasiewicz many valued logic with constants. In particular we focus on the structure of MV polynomials and MV polynomial functions on a given MV algebra.

27

Totaro, Burt. « Euler and algebraic geometry ». Bulletin of the American Mathematical Society 44, n^o 04 (22 juin 2007) : 541–60. http://dx.doi.org/10.1090/s0273-0979-07-01178-0.

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28

Jin, Lingfei, Yuan Luo et Chaoping Xing. « Repairing Algebraic Geometry Codes ». IEEE Transactions on Information Theory 64, n^o 2 (février 2018) : 900–908. http://dx.doi.org/10.1109/tit.2017.2773089.

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Bashmakova, I. G., et E. I. Slavutin. « Glimpses of Algebraic Geometry ». American Mathematical Monthly 104, n^o 1 (janvier 1997) : 62. http://dx.doi.org/10.2307/2974826.

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Gorodentsev, A. L., et A. N. Tyurin. « Abelian Lagrangian algebraic geometry ». Izvestiya : Mathematics 65, n^o 3 (30 juin 2001) : 437–67. http://dx.doi.org/10.1070/im2001v065n03abeh000334.

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31

Sergeraert, F. « Geometry and algebraic topology ». Mathematics and Computers in Simulation 42, n^o 4-6 (novembre 1996) : 459. http://dx.doi.org/10.1016/s0378-4754(96)00020-1.

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32

Winkler, Franz. « Algebraic computation in geometry ». Mathematics and Computers in Simulation 42, n^o 4-6 (novembre 1996) : 529–37. http://dx.doi.org/10.1016/s0378-4754(96)00028-6.

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Rota, Gian-Carlo. « Geometry of algebraic curves ». Advances in Mathematics 80, n^o 1 (mars 1990) : 134. http://dx.doi.org/10.1016/0001-8708(90)90021-e.

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Jun, Jaiung. « Algebraic geometry over hyperrings ». Advances in Mathematics 323 (janvier 2018) : 142–92. http://dx.doi.org/10.1016/j.aim.2017.10.043.

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35

Bashmakova, I. G., et E. I. Slavutin. « Glimpses of Algebraic Geometry ». American Mathematical Monthly 104, n^o 1 (janvier 1997) : 62–67. http://dx.doi.org/10.1080/00029890.1997.11990599.

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36

Gabber, Ofer, et Shane Kelly. « Points in algebraic geometry ». Journal of Pure and Applied Algebra 219, n^o 10 (octobre 2015) : 4667–80. http://dx.doi.org/10.1016/j.jpaa.2015.03.001.

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37

Grandau, Laura, et Ana C. Stephens. « Algebraic Thinking and Geometry ». Mathematics Teaching in the Middle School 11, n^o 7 (mars 2006) : 344–49. http://dx.doi.org/10.5951/mtms.11.7.0344.

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Research on the learning and teaching of algebra has recently been identified as a priority by members of the mathematics education research community (e.g., Ball 2003; Carpenter and Levi 2000; Kaput 1998; Olive, Izsak, and Blanton 2002). Rather than view algebra as an isolated course of study to be completed in the eighth or ninth grade, these researchers advocate the reconceptualization of algebra as a strand that weaves throughout other areas of mathematics in the K–12 curriculum.

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Newelski, Ludomir. « Geometry of *-Finite Types ». Journal of Symbolic Logic 64, n^o 4 (décembre 1999) : 1375–95. http://dx.doi.org/10.2307/2586784.

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AbstractAssume T is a superstable theory with < 2ℵ0 countable models. We prove that any *- algebraic type of -rank > 0 is m-nonorthogonal to a *-algebraic type of -rank 1. We study the geometry induced by m-dependence on a *-algebraic type p* of -rank 1. We prove that after some localization this geometry becomes projective over a division ring . Associated with p* is a meager type p. We prove that p is determined by p* up to nonorthogonality and that underlies also the geometry induced by forking dependence on any stationarization of p. Also we study some *-algebraic *-groups of -rank 1 and prove that any *-algebraic *-group of -rank 1 is abelian-by-finite.

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Toën, Bertrand, et Gabriele Vezzosi. « Homotopical algebraic geometry. II. Geometric stacks and applications ». Memoirs of the American Mathematical Society 193, n^o 902 (2008) : 0. http://dx.doi.org/10.1090/memo/0902.

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Daniyarova, Evelina Yur’evna, Alexei Georgievich Myasnikov et Vladimir Nikanorovich Remeslennikov. « Algebraic geometry over algebraic structures X : Ordinal dimension ». International Journal of Algebra and Computation 28, n^o 08 (décembre 2018) : 1425–48. http://dx.doi.org/10.1142/s0218196718400039.

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This work is devoted to interpretation of concepts of Zariski dimension of an algebraic variety over a field and of Krull dimension of a coordinate ring in algebraic geometry over algebraic structures of an arbitrary signature. Proposed dimensions are ordinal numbers (ordinals).

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Daniyarova, E. Yu, A. G. Myasnikov et V. N. Remeslennikov. « Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence ». Algebra and Logic 56, n^o 4 (septembre 2017) : 281–94. http://dx.doi.org/10.1007/s10469-017-9449-2.

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Baldwin, John T., et Andreas Mueller. « Autonomy of Geometry ». Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 11 (5 février 2020) : 5–24. http://dx.doi.org/10.24917/20809751.11.1.

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In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.

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Biswas, Indranil, et Sorin Dumitrescu. « Fujiki class 𝒞 and holomorphic geometric structures ». International Journal of Mathematics 31, n^o 05 (9 avril 2020) : 2050039. http://dx.doi.org/10.1142/s0129167x20500391.

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For compact complex manifolds with vanishing first Chern class that are compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class [Formula: see text], whose dimension is strictly larger than the algebraic dimension, we prove that it does not admit any holomorphic rigid geometric structure, and also it does not admit any holomorphic Cartan geometry of algebraic type. We prove that compact complex simply connected manifolds in Fujiki class [Formula: see text] and with vanishing first Chern class do not admit any holomorphic Cartan geometry of algebraic type.

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Ben-Bassat, Oren, et Kobi Kremnizer. « Non-Archimedean analytic geometry as relative algebraic geometry ». Annales de la faculté des sciences de Toulouse Mathématiques 26, n^o 1 (2017) : 49–126. http://dx.doi.org/10.5802/afst.1526.

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Belavin, A. A., et V. G. Knizhnik. « Algebraic geometry and the geometry of quantum strings ». Physics Letters B 168, n^o 3 (mars 1986) : 201–6. http://dx.doi.org/10.1016/0370-2693(86)90963-9.

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Ito, Atsushi, Makoto Miura et Kazushi Ueda. « Projective Reconstruction in Algebraic Vision ». Canadian Mathematical Bulletin 63, n^o 3 (13 novembre 2019) : 592–609. http://dx.doi.org/10.4153/s0008439519000687.

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AbstractWe discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

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KOSHKİN, Sergiy. « Algebraic geometry on imaginary triangles ». International Electronic Journal of Geometry 11, n^o 2 (30 novembre 2018) : 71–82. http://dx.doi.org/10.36890/iejg.545133.

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Miranda, Rick. « Triple Covers in Algebraic Geometry ». American Journal of Mathematics 107, n^o 5 (octobre 1985) : 1123. http://dx.doi.org/10.2307/2374349.

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Tyurin, N. A. « Lagrangian Geometry of Algebraic Manifolds ». Physics of Particles and Nuclei Letters 19, n^o 4 (26 juillet 2022) : 337–42. http://dx.doi.org/10.1134/s1547477122040215.

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Cabaña, Gustavo, María Chara, Ricardo Podestá et Ricardo Toledano. « On cyclic algebraic-geometry codes ». Finite Fields and Their Applications 82 (septembre 2022) : 102064. http://dx.doi.org/10.1016/j.ffa.2022.102064.

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Articles de revues sur le sujet « Geometry, Algebraic »

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