LEADER 03872nam 22006735 450 001 9910853992603321 005 20240912151506.0 010 $a3-031-54263-0 024 7 $a10.1007/978-3-031-54263-3 035 $a(MiAaPQ)EBC31230580 035 $a(Au-PeEL)EBL31230580 035 $a(DE-He213)978-3-031-54263-3 035 $a(CKB)31120757900041 035 $a(MiAaPQ)EBC31266853 035 $a(EXLCZ)9931120757900041 100 $a20240327d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHadamard Products of Projective Varieties /$fby Cristiano Bocci, Enrico Carlini 205 $a1st ed. 2024. 210 $cSpringer Nature$d2024 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (252 pages) 225 1 $aFrontiers in Mathematics,$x1660-8054 311 $a3-031-54262-2 327 $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. 330 $aThis monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn, is based on the operation of summing two vectors. However, other constructions are possible through a change of the basic operation. One remarkable case is based on the Hadamard product of two vectors. While secant varieties of algebraic varieties have been studied extensively and systematically, the same is not yet true for the Hadamard products of algebraic varieties. This monograph aims to bridge this gap in the literature. The topic is presented in a self-contained manner, and it is accessible to all readers with sound knowledge of Commutative Algebra and Algebraic Geometry. Both experienced researchers and students can profit from this monograph, which will guide them through the subject. The foundational aspects of the Hadamard products of algebraic varieties are covered and some connections both within and outside Algebraic Geometry are presented. The theoretical and algorithmic aspects of the subject are considered to demonstrate the effectiveness of the results presented. Thus, this monograph will also be useful to researchers in other fields, such as Algebraic Statistics, since it provides several algebraic and geometric results on such products. 410 0$aFrontiers in Mathematics,$x1660-8054 606 $aAlgebraic geometry 606 $aProjective geometry 606 $aComputer science$xMathematics 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebraic Geometry 606 $aProjective Geometry 606 $aSymbolic and Algebraic Manipulation 606 $aCommutative Rings and Algebras 615 0$aAlgebraic geometry. 615 0$aProjective geometry. 615 0$aComputer science$xMathematics. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aAlgebraic Geometry. 615 24$aProjective Geometry. 615 24$aSymbolic and Algebraic Manipulation. 615 24$aCommutative Rings and Algebras. 676 $a516.35 700 $aBocci$b Cristiano$0780979 701 $aCarlini$b Enrico$0966486 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910853992603321 996 $aHadamard Products of Projective Varieties$94158409 997 $aUNINA