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001 9780429451959
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020 _a9780429451959(e-book : PDF)
035 _a(OCoLC)1076543431
040 _aFlBoTFG
_cFlBoTFG
_erda
050 4 _aQA565
072 7 _aMAT
_x002000
_2bisacsh
072 7 _aMAT
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_2bisacsh
072 7 _aMAT
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072 7 _aPBF
_2bicscc
082 0 4 _a516.352
_223
100 1 _aFiedler - Le Touzé, Séverine ,
_eauthor.
245 1 0 _aPencils of Cubics and Algebraic Curves in the Real Projective Plane /
_cby Séverine Fiedler - Le Touzé.
250 _aFirst edition.
264 1 _aBoca Raton, FL :
_bChapman and Hall/CRC,
_c[2018].
264 4 _c©2019.
300 _a1 online resource (256 pages) :
_b169 illustrations, text file, PDF
336 _atext
_2rdacontent
337 _acomputer
_2rdamedia
338 _aonline resource
_2rdacarrier
504 _aIncludes bibliographical references and index.
505 0 0 _tRational pencils of cubics and configurations of six or seven points in RP -- Points, lines and conics in the plane -- Configurations of six points -- Configurations of seven points -- Pencils of cubics with eight base points lying in convex position in RP -- Pencils of cubics -- List of conics -- Link between lists and pencils -- Pencils with reducible cubics -- Classification of the pencils of cubics -- Tabulars -- Application to an interpolation problem -- Algebraic curves -- Hilberts 16th problem -- M-curves of degree 9 -- M-curves of degree 9 with deep nests -- M-curves of degree 9 with four or three nests -- M-curves of degree 9 or 11 with non-empty oval -- Curves of degree 11 with many nests -- Totally real pencils of curves.
520 3 _aPencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.
530 _aAlso available in print format.
650 7 _aMATHEMATICS / Geometry / General.
_2bisacsh
650 7 _aMATHEMATICS / Number Theory.
_2bisacsh
650 7 _aAlgebraic Geometry.
_2bisacsh
650 7 _aCombinatoirics.
_2bisacsh
650 7 _aCurves.
_2bisacsh
650 7 _aHilbert.
_2bisacsh
650 7 _aPencils.
_2bisacsh
650 7 _aTopology.
_2bisacsh
650 0 _aCurves, Algebraic.
650 0 _aCurves, Plane.
650 0 _aGeometry, Projective.
655 0 _aElectronic books.
710 2 _aTaylor and Francis.
776 0 8 _iPrint version:
_z9781138322578
856 4 0 _uhttps://www.taylorfrancis.com/books/9780429451959
_zClick here to view
999 _c126488
_d126488