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Добірка наукової літератури з теми "Geometry, Algebraic"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 29 липня 2024

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Статті в журналах з теми "Geometry, Algebraic"

Hacon, Christopher, Daniel Huybrechts, Yujiro Kawamata, and Bernd Siebert. "Algebraic Geometry." Oberwolfach Reports 12, no. 1 (2015): 783–836. http://dx.doi.org/10.4171/owr/2015/15.

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PLOTKIN, BORIS. "SOME RESULTS AND PROBLEMS RELATED TO UNIVERSAL ALGEBRAIC GEOMETRY." International Journal of Algebra and Computation 17, no. 05n06 (August 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.

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Tyurin, N. A. "Algebraic Lagrangian geometry: three geometric observations." Izvestiya: Mathematics 69, no. 1 (February 28, 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, no. 1 (March 17, 2010): 85–116. http://dx.doi.org/10.1007/s00032-010-0113-8.

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Toën, Bertrand. "Derived algebraic geometry." EMS Surveys in Mathematical Sciences 1, no. 2 (2014): 153–245. http://dx.doi.org/10.4171/emss/4.

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Debarre, Olivier, David Eisenbud, Gavril Farkas, and Ravi Vakil. "Classical Algebraic Geometry." Oberwolfach Reports 18, no. 2 (August 24, 2022): 1519–77. http://dx.doi.org/10.4171/owr/2021/29.

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Darke, Ian, and M. Reid. "Undergraduate Algebraic Geometry." Mathematical Gazette 73, no. 466 (December 1989): 351. http://dx.doi.org/10.2307/3619332.

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Debarre, Olivier, David Eisenbud, Frank-Olaf Schreyer, and Ravi Vakil. "Classical Algebraic Geometry." Oberwolfach Reports 9, no. 2 (2012): 1845–93. http://dx.doi.org/10.4171/owr/2012/30.

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Catanese, Fabrizio, Christopher Hacon, Yujiro Kawamata, and Bernd Siebert. "Complex Algebraic Geometry." Oberwolfach Reports 10, no. 2 (2013): 1563–627. http://dx.doi.org/10.4171/owr/2013/27.

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Debarre, Olivier, David Eisenbud, Gavril Farkas, and Ravi Vakil. "Classical Algebraic Geometry." Oberwolfach Reports 11, no. 3 (2014): 1695–745. http://dx.doi.org/10.4171/owr/2014/31.

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Дисертації з теми "Geometry, Algebraic"

Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.

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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu], wherein we consider three levels of spaces, each possessing a linear family of Poisson spaces. It is shown that there exist Poisson mappings between these levels. We consider the two cases where the underlying Riemann surface is an elliptic curve, as well as its degeneration to a Riemann sphere with two points identified (the trigonometric case). Background in necessary areas is provided.

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Lurie, Jacob 1977. "Derived algebraic geometry." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30144.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 191-193).
The purpose of this document is to establish the foundations for a theory of derived algebraic geometry based upon simplicial commutative rings. We define derived versions of schemes, algebraic spaces, and algebraic stacks. Our main result is a derived analogue of Artin's representability theorem, which provides a precise criteria for the representability of a moduli functor by geometric objects of these types.
by Jacob Lurie.
Ph.D.

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Balchin, Scott Lewis. "Augmented homotopical algebraic geometry." Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/40623.

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In this thesis we are interested in extending the theory of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. We introduce the concept of augmentation categories, which are a class of generalised Reedy categories. An augmentation category is a category which has enough structure that we can mirror the simplicial constructions which make up the theory of homotopical algebraic geometry. In particular, we construct a Quillen model structure on their presheaf categories, and introduce the concept of augmented hypercovers to define a local model structure on augmented presheaves. As an application, we show that a crossed simplicial group is an example of an augmentation category. The resulting augmented geometric theory can be thought of as being equivariant. Using this, we define equivariant cohomology theories as special mapping spaces in the category of equivariant stacks. We also define the SO(2)-equivariant derived stack of local systems by using a twisted nerve construction. Moreover, we prove that the category of planar rooted trees appearing in the theory of dendroidal sets is also an augmentation category. The augmented geometry over this setting should be thought of as being stable in the spectral sense of the word. Finally, we show that we can combine the two main examples presented using a categorical amalgamation construction.

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Rennie, Adam Charles. "Noncommutative spin geometry." Title page, contents and introduction only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phr4163.pdf.

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Dos, Santos João Pedro Pinto. "Fundamental groups in algebraic geometry." Thesis, University of Cambridge, 2006. https://www.repository.cam.ac.uk/handle/1810/252015.

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Slaatsveen, Anna Aarstrand. "Decoding of Algebraic Geometry Codes." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13729.

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Codes derived from algebraic curves are called algebraic geometry (AG) codes. They provide a way to correct errors which occur during transmission of information. This paper will concentrate on the decoding of algebraic geometry codes, in other words, how to find errors. We begin with a brief overview of some classical result in algebra as well as the definition of algebraic geometry codes. Then the theory of cyclic codes and BCH codes will be presented. We discuss the problem of finding the shortest linear feedback shift register (LFSR) which generates a given finite sequence. A decoding algorithm for BCH codes is the Berlekamp-Massey algorithm. This algorithm has complexity O(n^2) and provides a general solution to the problem of finding the shortest LFSR that generates a given sequence (which usually has running time O(n^3)). This algorithm may also be used for AG codes. Further we proceed with algorithms for decoding AG codes. The first algorithm for decoding algebraic geometry codes which we discuss is the so called basic decoding algorithm. This algorithm depends on the choice of a suitable divisor F. By creating a linear system of equation from the bases of spaces with prescribed zeroes and allowed poles we can find an error-locator function which contains all the error positions among its zeros. We find that this algorithm can correct up to (d* - 1 - g)/2 errors and have a running time of O(n^3). From this algorithm two other algorithms which improve on the error correcting capability are developed. The first algorithm developed from the basic algorithm is the modified algorithm. This algorithm depends on a restriction on the divisors which are used to build the code and an increasing sequence of divisors F1, ... , Fs. This gives rise to an algorithm which can correct up to (d*-1)/2 -S(H) errors and have a complexity of O(n^4). The correction rate of this algorithm is larger than the rate for the basic algorithm but it runs slower. The extended modified algorithm is created by the use of what we refer to as special divisors. We choose the divisors in the sequence of the modified algorithm to have certain properties so that the algorithm runs faster. When s(E) is the Clifford's defect of a set E of special divisor, the extended modified algorithm corrects up to (d*-1)/2 -s(E) which is an improvement from the basic algorithm. The running time of the algorithm is O(n^3). The last algorithm we present is the Sudan-Guruswami list decoding algorithm. This algorithm searches for all possible code words within a certain distance from the received word. We show that AG codes are (e,b)-decodable and that the algorithm in most cases has a a higher correction rate than the other algorithms presented here.

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Birkar, Caucher. "Topics in modern algebraic geometry." Thesis, University of Nottingham, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.421475.

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Lundman, Anders. "Topics in Combinatorial Algebraic Geometry." Doctoral thesis, KTH, Matematik (Avd.), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-176878.

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This thesis consists of six papers in algebraic geometry –all of which have close connections to combinatorics. In Paper A we consider complete smooth toric embeddings X ↪ P^N such that for a fixed positive integer k the t-th osculating space at every point has maximal dimension if and only if t ≤ k. Our main result is that this assumption is equivalent to that X ↪ P^N is associated to a Cayley polytope of order k having every edge of length at least k. This result generalizes an earlier characterisation by David Perkinson. In addition we prove that the above assumptions are equivalent to requiring that the Seshadri constant is exactly k at every point of X, generalizing a result of Atsushi Ito. In Paper B we introduce H-constants that measure the negativity of curves on blow-ups of surfaces. We relate these constants to the bounded negativity conjecture. Moreover we provide bounds on H-constants when restricting to curves which are a union of lines in the real or complex projective plane. In Paper C we study Gauss maps of order k for k > 1, which maps a point on a variety to its k-th osculating space at that point. Our main result is that as in the case k = 1, the higher order Gauss maps are finite on smooth varieties whose k-th osculating space is full-dimensional everywhere. Furthermore we provide convex geometric descriptions of these maps in the toric setting. In Paper D we classify fat point schemes on Hirzebruch surfaces whose initial sequence are of maximal or close to maximal length. The initial degree and initial sequence of such schemes are closely related to the famous Nagata conjecture. In Paper E we introduce the package LatticePolytopes for Macaulay2. The package extends the functionality of Macaulay2 for compuations in toric geometry and convex geometry. In Paper F we compute the Seshadri constant at a general point on smooth toric surfaces satisfying certain convex geometric assumptions on the associated polygons. Our computations relate the Seshadri constant at the general point with the jet seperation and unnormalised spectral values of the surfaces at hand.
Den här avhandlingen utgörs av sex artiklar inom algebraisk geometri som är nära kopplade till kombinatorik. I artikel A betraktar vi kompletta inbäddningar av glatta toriska variteter X ↪ PN sådana att för något fixt heltal k är det t-te oskulerande rummet i varje punkt av maximal dimension om och endast om t ≤ k. Vårt huvudresultat är att detta antagande är ekvivalent med att den polytop som motsvarar inbäddningen är en Cayleypolytop av ordning k, vars samtliga kanter har längd åtminstonde k. Detta resultat generaliserar en tidigare känd karaktärisering av David Perkinson. Vi visar även att ovanstående antagande är ekvivalent med antagandet att Seshadri- konstanten är lika med k i varje punkt i X. Därmed generaliserar vårt resultat ett tidigare resultat av Atsushi Ito. I artikel B introducerar vi H-konstanter, vilka mäter negativiteten av kurvor på uppblåsningar av ytor. Vi relaterar dessa konstanter till den begränsade negativitetsförmodan. Vidare erhåller vi begränsningar för konstanterna när vi enbart betraktar unioner av linjer i det reella och komplexa projektiva planet. I artikel C studerar vi Gaussavbildningen av ordning k, för k > 1, som avbildar en punkt i en varitet på det k-te oskulerande rummet i samma punkt. Vårt huvudresultat är att, i likhet med fallet k = 1, är dessa högre ordningens Gaussavbildningar ändliga på glatta variteter vars k-te oskulerande rum är fulldimensionellt överallt. Vidare ger vi konvexgeometriska beskrivningar av dessa avbildningar för toriska variteter. I artikel D klassificerar vi scheman av tjocka punkter på Hirzebruchytor vars initalsekvenser är av maximal eller nära maximal längd. Intitialgraden och initialsekvensen för sådana scheman är nära relaterade till den välkända Nagata- förmodan. I artikel E introducerar vi paketet LatticePolytopes till Macaulay2. Detta paket utökar funktionaliteten i Macaulay2 för beräkningar inom torisk och konvex geometri. I artikel F beräknar vi Seshadrikonstanten i generella punkter på glatta toriska ytor som uppfyller vissa konvexgeometriska villkor på de associerade polygonerna. Våra beräkningar koppplar samman Seshadrikonstanten i en generell punkt med jetsepareringen och det icke-normaliserade spektralvärdet hos ytorna.

QC 20151112

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Hu, Jiawei. "Partial actions in algebraic geometry." Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/273459.

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We introduce geometrically partial comodules over coalgebras in monoidal categories, as an alternative notion to the notion of partial action and coaction of Hopf algebras introduced by Caenepeel and Janssen. We show that our new notion suits better if one wants to describe phenomena of partial actions in algebraic geometry. We show that under mild conditions, the category of geometric partial comodules is complete and cocomplete and the category of partial comodules over a Hopf algebra is lax monoidal. We develop a Hopf-Galois theory for geometric partial coactions to illustrate that our new notion might be a useful additional tool in Hopf algebra theory.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Garcia-Puente, Luis David. "Algebraic Geometry of Bayesian Networks." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11133.

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We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.
Ph. D.

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Книги з теми "Geometry, Algebraic"

Cox, David A. Using algebraic geometry. New York: Springer, 1998.

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Cox, David A. Using algebraic geometry. 2nd ed. New York: Springer, 2005.

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Lefschetz, Solomon. Algebraic geometry. Mineola, N.Y: Dover Publications, 2005.

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Harris, Joe. Algebraic Geometry. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2189-8.

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Sommese, Andrew John, Aldo Biancofiore, and Elvira Laura Livorni, eds. Algebraic Geometry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083328.

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Abramovich, D., A. Bertram, L. Katzarkov, R. Pandharipande, and M. Thaddeus, eds. Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/pspum/080.1.

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Keum, JongHae, and Shigeyuki Kondō, eds. Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/conm/422.

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Kurke, H., and J. H. M. Steenbrink, eds. Algebraic Geometry. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0685-3.

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Perrin, Daniel. Algebraic Geometry. London: Springer London, 2008. http://dx.doi.org/10.1007/978-1-84800-056-8.

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Частини книг з теми "Geometry, Algebraic"

Stillwell, John. "Algebraic Geometry." In Undergraduate Texts in Mathematics, 85–97. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55193-3_6.

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Wells, Raymond O. "Algebraic Geometry." In Differential and Complex Geometry: Origins, Abstractions and Embeddings, 5–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58184-2_1.

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Mazzola, Guerino. "Algebraic Geometry." In The Topos of Music IV: Roots, 1411–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64495-0_6.

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Suzuki, Joe. "Algebraic Geometry." In WAIC and WBIC with Python Stan, 153–73. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3841-4_7.

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Wallach, Nolan R. "Algebraic Geometry." In Universitext, 3–29. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65907-7_1.

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Elliott, David L. "Algebraic Geometry." In Bilinear Control Systems, 247–50. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1023/b101451_11.

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Beshaj, Lubjana. "Algebraic Geometry." In Mathematics in Cyber Research, 97–132. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9780429354649-3.

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Suzuki, Joe. "Algebraic Geometry." In WAIC and WBIC with R Stan, 151–70. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-3838-4_7.

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Harris, Joe. "Algebraic Groups." In Algebraic Geometry, 114–29. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-2189-8_10.

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Bogomolov, F. A., and A. N. Landia. "2-Cocycles and Azumaya algebras under birational transformations of algebraic schemes." In Algebraic Geometry, 1–5. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0685-3_1.

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Тези доповідей конференцій з теми "Geometry, Algebraic"

Sharir, Micha. "Algebraic Techniques in Geometry." In ISSAC '18: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3208976.3209028.

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Roan, Shi-shyr. "Algebraic Geometry and Physics." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0042.

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LÊ, DŨNG TRÁNG, and BERNARD TEISSIER. "GEOMETRY OF CHARACTERISTIC VARIETIES." In Algebraic Approach to Differential Equations. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814273244_0003.

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Borghesi, Simone. "Cohomology operations and algebraic geometry." In International Conference in Homotopy Theory. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2007.10.75.

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BIRKAR, CAUCHER. "BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0068.

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Soleev, A., and N. Soleeva. "Power geometry and algebraic equations." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823880.

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Daniyarova, E., A. Myasnikov, and V. Remeslennikov. "Unification theorems in algebraic geometry." In A Festschrift in Honor of Anthony Gaglione. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793416_0007.

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Barczik, Günter, Oliver Labs, and Daniel Lordick. "Algebraic Geometry in Architectural Design." In eCAADe 2009: Computation: The New Realm of Architectural Design. eCAADe, 2009. http://dx.doi.org/10.52842/conf.ecaade.2009.455.

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Wampler, Charles W. "Numerical algebraic geometry and kinematics." In ISSAC07: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2007. http://dx.doi.org/10.1145/1277500.1277506.

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Cariñena, J. F., A. Ibort, G. Marmo, G. Morandi, Fernando Etayo, Mario Fioravanti, and Rafael Santamaría. "Geometrical description of algebraic structures: Applications to Quantum Mechanics." In GEOMETRY AND PHYSICS: XVII International Fall Workshop on Geometry and Physics. AIP, 2009. http://dx.doi.org/10.1063/1.3146238.

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Звіти організацій з теми "Geometry, Algebraic"

Bashelor, Andrew Clark. Enumerative Algebraic Geometry: Counting Conics. Fort Belvoir, VA: Defense Technical Information Center, May 2005. http://dx.doi.org/10.21236/ada437184.

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Stiller, Peter. Algebraic Geometry and Computational Algebraic Geometry for Image Database Indexing, Image Recognition, And Computer Vision. Fort Belvoir, VA: Defense Technical Information Center, October 1999. http://dx.doi.org/10.21236/ada384588.

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Thompson, David C., Joseph Maurice Rojas, and Philippe Pierre Pebay. Computational algebraic geometry for statistical modeling FY09Q2 progress. Office of Scientific and Technical Information (OSTI), March 2009. http://dx.doi.org/10.2172/984161.

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Bates, Daniel J., Daniel A. Brake, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler. Real Numerical Algebraic Geometry: Finding All Real Solutions of a Polynomial System. Fort Belvoir, VA: Defense Technical Information Center, February 2014. http://dx.doi.org/10.21236/ada597283.

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Rabier, Patrick J., and Werner C. Rheinboldt. A Geometric Treatment of Implicit Differential-Algebraic Equations. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada236991.

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Watts, Paul. Differential geometry on Hopf algebras and quantum groups. Office of Scientific and Technical Information (OSTI), December 1994. http://dx.doi.org/10.2172/89507.

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods in Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada260967.

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Yau, Stephen S. PDE, Differential Geometric and Algebraic Methods for Nonlinear Filtering. Fort Belvoir, VA: Defense Technical Information Center, February 1996. http://dx.doi.org/10.21236/ada310330.

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Mundy, Joseph L. Representation and Recognition with Algebraic Invariants and Geometric Constraint Models. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada282926.

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Mundy, Joseph L. Representation and Recognition with Algebraic Invariants and Geometric Constraint Models. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada271395.

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