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Relevant bibliographies by topics / Algebraic intersection

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Academic literature on the topic 'Algebraic intersection'

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Published: 4 May 2024

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Journal articles on the topic "Algebraic intersection"

1

Geske, Christian. "Algebraic intersection spaces." Journal of Topology and Analysis 12, no. 04 (2019): 1157–94. http://dx.doi.org/10.1142/s1793525319500778.

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We define a variant of intersection space theory that applies to many compact complex and real analytic spaces [Formula: see text], including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the (reduced) chain complexes of known topological intersection spaces in the case that both exist. We next analyze “local duality obstructions,” which we can choose to vanish, and verify that algebraic intersection spaces satisfy duality in the absence of these obstructions. We conclude by defining an untwisted algebraic intersection space pairing, whose signature is equal to the Novikov signature of the complement in [Formula: see text] of a tubular neighborhood of the singular set.

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Patrikalakis, N. M., and P. V. Prakash. "Surface Intersections for Geometric Modeling." Journal of Mechanical Design 112, no. 1 (1990): 100–107. http://dx.doi.org/10.1115/1.2912565.

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Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution procedure. Using turning and singular points, the intersection problem can be partitioned into subdomains that can be processed independently and which involve intersection segments that can be traced with faceting methods. This partitioning and the tracing of individual segments is carried out using an adaptive subdivision algorithm for Bezier/B-spline surfaces followed by Newton correction of the approximation. The method has been successfully tested in tracing complex algebraic curves and in solving actual intersection problems with diverse features.

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Brasselet, J. P. "Intersection of algebraic cycles." Journal of Mathematical Sciences 82, no. 5 (1996): 3625–32. http://dx.doi.org/10.1007/bf02362566.

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LÓPEZ, HIRAM H., and RAFAEL H. VILLARREAL. "COMPLETE INTERSECTIONS IN BINOMIAL AND LATTICE IDEALS." International Journal of Algebra and Computation 23, no. 06 (2013): 1419–29. http://dx.doi.org/10.1142/s0218196713500288.

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For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set-theoretic complete intersections. In characteristic zero, we show that an arbitrary lattice ideal which is a binomial set-theoretic complete intersection is a complete intersection.

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MANOCHA, DINESH, and JOHN F. CANNY. "A NEW APPROACH FOR SURFACE INTERSECTION." International Journal of Computational Geometry & Applications 01, no. 04 (1991): 491–516. http://dx.doi.org/10.1142/s0218195991000311.

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Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling. However, surface intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good surface intersection technique has to balance three conflicting goals of accuracy, robustness and efficiency. In this paper, we formulate the problems of curve and surface intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The projected set can be expressed as a matrix determinant. The matrix itself, rather than its symbolic determinant, is used as the representation for the algebraic set in the lower dimensional space. This is a much more compact and efficient representation. Given such a representation, we perform matrix operations for evaluation and use results from linear algebra for geometric operations on the intersection curve. Most of the operations involve evaluating numeric determinants and computing the rank, kernel and eigenvalues of matrices. The accuracy of such operations can be improved by pivoting or other numerical techniques. We use this representation for inversion operation, computing the intersection of curves and surfaces and tracing the intersection curve of two surfaces in lower dimension.

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Yokura, Shoji. "Algebraic cycles and intersection homology." Proceedings of the American Mathematical Society 103, no. 1 (1988): 41. http://dx.doi.org/10.1090/s0002-9939-1988-0938641-x.

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Abhyankar, Shreeram S., Srinivasan Chandrasekar, and Vijaya Chandru. "Improper intersection of algebraic curves." ACM Transactions on Graphics 9, no. 2 (1990): 147–59. http://dx.doi.org/10.1145/78956.78957.

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Mandal, Satya, and Yong Yang. "Intersection theory of algebraic obstructions." Journal of Pure and Applied Algebra 214, no. 12 (2010): 2279–93. http://dx.doi.org/10.1016/j.jpaa.2010.02.027.

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Levine, Marc. "Intersection theory in algebraic cobordism." Journal of Pure and Applied Algebra 221, no. 7 (2017): 1645–90. http://dx.doi.org/10.1016/j.jpaa.2016.12.022.

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Sederberg, T. W. "Algorithm for algebraic curve intersection." Computer-Aided Design 21, no. 9 (1989): 547–54. http://dx.doi.org/10.1016/0010-4485(89)90015-8.

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Dissertations / Theses on the topic "Algebraic intersection"

1

Silberstein, Aaron. "Anabelian Intersection Theory." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10141.

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Let F be a field finitely generated and of transcendence degree 2 over \(\bar{\mathbb{Q}}\). We describe a correspondence between the smooth algebraic surfaces X defined over \(\bar{\mathbb{Q}}\) with field of rational functions F and Florian Pop’s geometric sets of prime divisors on \(Gal(\bar{F}/F)\), which are purely group-theoretical objects. This allows us to give a strong anabelian theorem for these surfaces. As a corollary, for each number field K, we give a method to construct infinitely many profinite groups \(\Gamma\) such that \(Out_{cont} (\Gamma)\) is isomorphic to \(Gal(\bar{K}/K)\), and we find a host of new categories which answer the Question of Ihara/Conjecture of Oda-Matsumura.<br>Mathematics

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Nichols, Margaret E. "Intersection Number of Plane Curves." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385.

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Garay-Lopez, Cristhian Emmanuel. "Tropical intersection theory, and real inflection points of real algebraic curves." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066364/document.

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Cette thèse est divisée en deux parties principales. D’abord on étudie des relations entre les théories d’intersection en géométrie tropicale et géométrie algébrique. Puis on étudie la question des possibilités pour la distribution de points d’inflexion réels associés à un système linéaire réel défini sur une courbe algébrique réelle lisse. Dans la première partie, nous présentons des nouveaux résultats reliant les théories d’intersection algébrique et tropicale dans une variété algébrique très affine définie sur un corps non-archimédien particulier (dit corps de Mal’cev-Neumann). Le résultat principale concerne l’intersection d’un cycle algébrique de dimension 1 dans une variété à tropicalisation simple avec un diviseur de Cartier. Dans la deuxième partie, nous obtenons d’abord une caractérisation de la répartition des points d’inflexion réels d’un système linéaire complet de degré d>1 sur une courbe elliptique réelle lisse. Puis nous étudions quelques courbes réelles non-hyperelliptiques canoniques de genre 4 dans l’espace projectif de dimension 3. Nous obtenons une formule qui relie le nombre de points de Weierstrass réels d’une telle courbe avec la caractéristique d’Euler-Poincaré d’un certain espace topologique. Finalement, en utilisant la technique du Patchworking (dû à O. Viro), on construit un exemple de courbe réelle, lisse, non-hyperelliptique de genre 4 ayant 30 points de Weierstrass réels<br>This thesis is divided in two main parts. First, we study the relationships between intersection theories in tropical and algebraic geometry. Then, we study the question of the possibilities for the distribution of the real inflection points associated to a real linear system defined on a smooth real algebraic curve. In the first part, we present new results linking algebraic and tropical intersection theories over a very-affine algebraic variety defined over a particular non-Archimedean field (known as Mal’cev-Newmann field). The main result concerns the intersection of a one-dimensional algebraic cycle with a Cartier divisor in a variety with simple tropicalization. In the second part, we obtain first a characterization of the distribution of real inflection points associated to a real complete linear system of degree d>1 defined over a smooth real elliptic curve. Then we study some canonical, non-hyperelliptic real algebraic curves of genus 4 in a 3-dimensional projective space. We obtain a formule that relies the amount of real Weierstrass points of such a curve with the Euler-Poincaré characteristic of certain topological space. Finally, using O. Viro’s Patch-working technique, we construct an example of a smooth, non-hyperelliptic real algebraic curve of genus 4 having 30 real Weierstrass points

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Ihringer, Ferdinand [Verfasser]. "Finite geometry intersecting algebraic combinatorics : an investigation of intersection problems related to Erdös-Ko-Rado theorems on Galois geometries with help from algebraic combinatorics / Ferdinand Ihringer." Gießen : Universitätsbibliothek, 2015. http://d-nb.info/1076005918/34.

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Kioulos, Charalambos. "From Flag Manifolds to Severi-Brauer Varieties: Intersection Theory, Algebraic Cycles and Motives." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40716.

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The study of algebraic varieties originates from the study of smooth manifolds. One of the focal points is the theory of differential forms and de Rham cohomology. It’s algebraic counterparts are given by algebraic cycles and Chow groups. Linearizing and taking the pseudo-abelian envelope of the category of smooth projective varieties, one obtains the category of pure motives. In this thesis, we concentrate on studying the pure Chow motives of Severi-Brauer varieties. This has been a subject of intensive investigation for the past twenty years, with major contributions done by Karpenko, [Kar1], [Kar2], [Kar3], [Kar4]; Panin, [Pan1], [Pan2]; Brosnan, [Bro1], [Bro2]; Chernousov, Merkurjev, [Che1], [Che2]; Petrov, Semenov, Zainoulline, [Pet]; Calmès, [Cal]; Nikolenko, [Nik]; Nenashev, [Nen]; Smirnov, [Smi]; Auel, [Aue]; Krashen, [Kra]; and others. The main theorem of the thesis, presented in sections 4.3 and 4.4, extends the result of Zainoulline et al. in the paper [Cal] by providing new examples of motivic decompositions of generalized Severi-Brauer varieties.

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Treisman, Zachary. "Arc spaces and rational curves /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5780.

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Hilmar, Jan. "Intersection of algebraic plane curves : some results on the (monic) integer transfinite diameter." Thesis, University of Edinburgh, 2008. http://hdl.handle.net/1842/3843.

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Part I discusses the problem of determining the set of intersection points, with corresponding multiplicities, of two algebraic plane curves. We derive an algorithm based on the Euclidean Algorithm for polynomials and show how to use it to find the intersection points of two given curves. We also show that an easy proof of Bézout’s Theorem follows. We then discuss how, for curves with rational coefficients, this algorithm can bemodified to find the intersection points with coordinates expressed in terms of algebraic extensions of the rational numbers. Part II deals with the problem of determining the (monic) integer transfinite diameter of a given real interval. We show how this problem relates to the problem of determining the structure of the spectrum of normalised leading coefficients of polynomials with integer coefficients and all roots in the given interval. We then find dense regions of this spectrum for a number of intervals and discuss algorithms for finding discrete subsets of the spectrum for the interval [0,1]. This leads to an improvement in the known upper bound for the integer transfinite diameter. Finally, we discuss the connection between the infimum of the spectrum and the monic integer transfinite diameter.

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Mitchell, W. P. R. "p-Fold intersection points and their relation with #pi#'s(MU(n))." Thesis, University of Manchester, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377731.

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Wotzlaw, Lorenz. "Intersection cohomology of hypersurfaces." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2008. http://dx.doi.org/10.18452/15719.

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Bekannte Theoreme von Carlson und Griffiths gestatten es, die Variation von Hodgestrukturen assoziiert zu einer Familie von glatten Hyperflächen sowie das Cupprodukt auf der mittleren Kohomologie explizit zu beschreiben. Wir benutzen M. Saitos Theorie der gemischten Hodgemoduln, um diesen Kalkül auf die Variation der Hodgestruktur der Schnittkohomologie von Familien nodaler Hyperflächen zu verallgemeinern.<br>Well known theorems of Carlson and Griffiths provide an explicit description of the variation of Hodge structures associated to a family of smooth hypersurfaces together with the cupproduct pairing on the middle cohomology. We give a generalization to families of nodal hypersurfaces using M. Saitos theory of mixed Hodge modules.

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Ernstroem, Lars, Shoji Yokura, and yokura@sci kagoshima-u. ac jp. "Bivariant Chern-Schwartz-MacPherson Classes with Values in Chow Groups." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi891.ps.

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Books on the topic "Algebraic intersection"

1

Armand, Borel, ed. Intersection cohomology. Birkhäuser, 2008.

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2

Ellingsrud, Geir. Recent Progress in Intersection Theory. Birkhäuser Boston, 2000.

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1948-, Masser David William, ed. Some problems of unlikely intersections in arithmetic and geometry. Princeton University Press, 2012.

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4

Cho, Yŏng-hyŏn. Taesu kihahak: Wanjŏn kyochʻa rŭl chungsim ŭro. Minŭmsa, 1991.

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Mandal, Satya. Projective modules and complete intersections. Springer, 1997.

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Rumely, Robert S. Capacity theory on algebraic curves. Springer-Verlag, 1989.

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Zeuthen Symposium (1989 Mathematical Institute of the University of Copenhagen). Enumerative algebraic geometry: Proceedings of the 1989 Zeuthen Symposium. Edited by Zeuthen H. G. 1839-1920, Kleiman Steven L, Thorup Anders 1943-, and Statens naturvidenskabelige forskningsråd (Denmark). American Mathematical Society, 1991.

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8

Uwe, Storch, ed. Regular sequences and resultants. A.K. Peters, 2001.

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9

G, Rodicio Antonio, ed. Smoothness, regularity and complete intersection. Cambridge University Press, 2010.

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Kirwan, Frances. An introductionto intersection homology theory. Longman Scientific & Technical, 1988.

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Book chapters on the topic "Algebraic intersection"

1

Fulton, William. "Families of Algebraic Cycles." In Intersection Theory. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1700-8_11.

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Fulton, William. "Algebraic, Homological, and Numerical Equivalence." In Intersection Theory. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1700-8_20.

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Shafarevich, Igor R. "Intersection Numbers." In Basic Algebraic Geometry 1. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57908-0_4.

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Shafarevich, Igor R. "Intersection Numbers." In Basic Algebraic Geometry 1. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37956-7_4.

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Awange, Joseph L., and Béla Paláncz. "Positioning by Intersection Methods." In Geospatial Algebraic Computations. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25465-4_17.

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Holme, Audun. "Intersection Theory." In A Royal Road to Algebraic Geometry. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-19225-8_18.

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Brieskorn, Egbert, and Horst Knörrer. "The intersection of plane curves." In Plane Algebraic Curves. Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5097-1_6.

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Awange, Joseph L., Erik W. Grafarend, Béla Paláncz, and Piroska Zaletnyik. "Positioning by intersection methods." In Algebraic Geodesy and Geoinformatics. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12124-1_14.

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Brieskorn, Egbert, and Horst Knörrer. "6. The intersection of plane curves." In Plane Algebraic Curves. Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_6.

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Jongeneel, Wouter, and Emmanuel Moulay. "Algebraic Topology." In SpringerBriefs in Electrical and Computer Engineering. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30133-9_4.

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AbstractIn this chapter we briefly introduce important concepts from homology theory and we highlight how some results from Chap. 3 can be understood through the lens of algebraic topology. This chapter accumulates in showing that the Euler characteristic can be understood by means of CW complexes, homology or intersection theory.

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Conference papers on the topic "Algebraic intersection"

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Hovey, Mark. "Intersection homological algebra." In New topological contexts for Galois theory and algebraic geometry. Mathematical Sciences Publishers, 2009. http://dx.doi.org/10.2140/gtm.2009.16.133.

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Busé, Laurent, and Ibrahim Nonkané. "Discriminants of Complete Intersection Space Curves." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. ACM, 2017. http://dx.doi.org/10.1145/3087604.3087635.

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Noack, Benjamin, Joris Sijs, and Uwe D. Hanebeck. "Algebraic analysis of data fusion with ellipsoidal intersection." In 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI). IEEE, 2016. http://dx.doi.org/10.1109/mfi.2016.7849515.

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Abhyankar, S. S., S. Chandrasekar, and V. Chandru. "Degree complexity bounds on the intersection of algebraic curves." In the fifth annual symposium. ACM Press, 1989. http://dx.doi.org/10.1145/73833.73843.

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Chen, Xiao-Diao, Jun-Hai Yong, Jean-Claude Paul, and Jiaguang Sun. "Intersection Testing between an Ellipsoid and an Algebraic Surface." In 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics. IEEE, 2007. http://dx.doi.org/10.1109/cadcg.2007.4407853.

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Blechschmidt, James L., and D. Nagasuru. "The Use of Algebraic Functions As a Solid Modeling Alternative: An Investigation." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0005.

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Abstract An investigation of surface and solid modeling using a single unbounded algebraic function for objects requiring free form surfaces is discussed. The purpose of this investigation is to determine if a single closed algebraic function can be effectively used to represent objects. Curve fitting techniques are developed. Surfaces using implicit algebraic functions are developed using the techniques of revolution about an axis and extrusion along a curve segment. Infinite extrusions of a planar cross section along an axis of the form y = f(x) are developed. The boolean operators of union, intersection, and difference are developed using the defining function form of algebraic functions. All of the operations have been accomplished in algebra using polynomial multiplication, addition, and subtraction. Examples of all the operations are presented.

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Blechschmidt, James L., and Chung-Hsing Lee. "The Design and Analysis of Cam Profiles Using Algebraic Functions." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0150.

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Abstract A new method for the design and analysis of cam profiles is developed and demonstrated in this paper using algebraic functions in two variables. A technique for the construction of the cam profile directly without using the lift curve is developed. The basis for this analysis is the use of Boolean operators in algebra using a form of algebraic function called the defining function. Using simple quadratic curves such as circles, ellipses, and slabs, more complicated cam profiles are constructed using the Boolean operators of union, intersection, and difference. The resulting closed algebraic curve is converted to the standard implicit form for follower analysis. We show that cam profiles using constraints on the lift at a specific angular rotation can be developed. Examples of all the operations are demonstrated.

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Marsden, Gary C., Ted Shaneyfelt, Sadik Esener, and Sing H. Lee. "Optoelectronic relational algebraic processor." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.fbb4.

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The dual scale topology optoelectronic processor (DSTOP) was developed for generalized matrix algebra.1 Vector outer products are a particularly useful feature of the DSTOP architecture. Since the computation is performed electronically, a generalized function may be substituted for conventional numerical multiplication; this is especially useful in symbolic computations such as those required in relational databases. We have developed algorithms appropriate for DSTOP that use generalized outer products in the execution of relational algebraic operations.2 The DSTOP processor serves as a decision subsystem in a relational database machine. The DSTOP relational algebraic processor is well suited to interface with 3D optical storage devices such as optical disks, photorefractive crystals or two-photon memories. The operations performed include joins, set difference, union, intersection and set division. Duplicate removal may also be performed in the support of the projection relational operator. The remaining relational operators, selection and Cartesian product, are not included. Cartesian products require no decision mechanism while selection, which is a unary operator, is best performed on a smaller, front end processor.

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Chiang, L. E., and D. J. Wilde. "A Method to Find Parametric Bicubic Surface Intersections." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0026.

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Abstract This paper discusses the problem of finding the intersection between two bicubic parametric patches. This is an important problem in Geometric Modeling since bicubic parametric patches are the most common design element in this field. A brief discussion of the existing approaches such as surface subdivision and curve tracing is given first. Next the algebraic solution to solve the intersection between cubic parametric curves is described in order to lay the foundations for an original algebraic method to solve the analog surface case.

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Ganter, M. A., D. W. Storti, and M. T. Ensz. "On Algebraic Methods for Implicit Swept Solids With Finite Extent." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0411.

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Abstract In this paper, we consider geometric construction of swept solids using algebraic methods based on classical envelope theory. Methods are presented for construction of algebraic swept solids with finite extent and variable geometry. Problems of local and global self-intersection (undercutting in the terminology of cam design) are considered, and void removal concepts are demonstrated. Examples presented include offsets of Bezier curves and twisted sweeps with ellipsoidal primitives.

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Reports on the topic "Algebraic intersection"

1

Borgwardt, Stefan, and Rafael Peñaloza. Complementation and Inclusion of Weighted Automata on Infinite Trees: Revised Version. Technische Universität Dresden, 2011. http://dx.doi.org/10.25368/2022.180.

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Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.

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Borgwardt, Stefan, and Rafael Peñaloza. Complementation and Inclusion of Weighted Automata on Infinite Trees. Technische Universität Dresden, 2010. http://dx.doi.org/10.25368/2022.178.

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Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation and inclusion for weighted automata on infinite trees and show that they are not harder than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally.

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