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001 978-3-031-54263-3
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020 _a9783031542633
_9978-3-031-54263-3
024 7 _a10.1007/978-3-031-54263-3
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
100 1 _aBocci, Cristiano.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_974055
245 1 0 _aHadamard Products of Projective Varieties
_h[electronic resource] /
_cby Cristiano Bocci, Enrico Carlini.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXIX, 243 p. 9 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aFrontiers in Mathematics,
_x1660-8054
505 0 _aHadamard products -- Linear spaces -- Not generic cases in P2 -- Grids and rulings -- Degenerate varieties -- Hypersurfaces -- Binomial varieties -- Hilbert functions -- Star configurations -- Gorenstein sets of points in P3 -- Pure Commutative Algebra -- Open questions.
520 _aThis monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn, is based on the operation of summing two vectors. However, other constructions are possible through a change of the basic operation. One remarkable case is based on the Hadamard product of two vectors. While secant varieties of algebraic varieties have been studied extensively and systematically, the same is not yet true for the Hadamard products of algebraic varieties. This monograph aims to bridge this gap in the literature. The topic is presented in a self-contained manner, and it is accessible to all readers with sound knowledge of Commutative Algebra and Algebraic Geometry. Both experienced researchers and students can profit from this monograph, which will guide them through the subject. The foundational aspects of the Hadamard products of algebraic varieties are covered and some connections both within and outside Algebraic Geometry are presented. The theoretical and algorithmic aspects of the subject are considered to demonstrate the effectiveness of the results presented. Thus, this monograph will also be useful to researchers in other fields, such as Algebraic Statistics, since it provides several algebraic and geometric results on such products.
650 0 _aAlgebraic geometry.
650 0 _aProjective geometry.
_974056
650 0 _aComputer science
_xMathematics.
_964041
650 0 _aCommutative algebra.
_970151
650 0 _aCommutative rings.
_970152
650 1 4 _aAlgebraic Geometry.
650 2 4 _aProjective Geometry.
_974057
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aCommutative Rings and Algebras.
_970156
700 1 _aCarlini, Enrico.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_974058
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031542626
776 0 8 _iPrinted edition:
_z9783031542640
830 0 _aFrontiers in Mathematics,
_x1660-8054
_972228
856 4 0 _uhttps://doi.org/10.1007/978-3-031-54263-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c58681
_d58681