03712nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203072001600226100008600242245010800328250001800436264007300454300004300527336002600570337002600596338003600622347002400658490004100682505027600723520152600999650002402525650003202549650004202581650003202623650003002655650002402685650003202709650004102741650004302782700008502825710003402910773002602944776003602970776003603006830004803042856004603090912001403136912001503150999001703165978-3-031-54263-3DE-He21320251030111746.0cr nn 008mamaa240327s2024    sz |    s    |||| 0|eng d  a97830315426339978-3-031-54263-37 a10.1007/978-3-031-54263-32doi 4aQA564-609 7aPBMW2bicssc 7aMAT0120102bisacsh 7aPBMW2thema1 aBocci, Cristiano.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97405510aHadamard Products of Projective Varietiesh[electronic resource] /cby Cristiano Bocci, Enrico Carlini.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXIX, 243 p. 9 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aFrontiers in Mathematics,x1660-80540 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.  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. 0aAlgebraic geometry. 0aProjective geometry.974056 0aComputer sciencexMathematics.964041 0aCommutative algebra.970151 0aCommutative rings.97015214aAlgebraic Geometry.24aProjective Geometry.97405724aSymbolic and Algebraic Manipulation.24aCommutative Rings and Algebras.9701561 aCarlini, Enrico.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9740582 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154262608iPrinted edition:z9783031542640 0aFrontiers in Mathematics,x1660-805497222840uhttps://doi.org/10.1007/978-3-031-54263-3  aZDB-2-SMA  aZDB-2-SXMS  c58681d58681