LEADER 03471nam 2200529 450 001 996466407703316 005 20220613100713.0 010 $a3-030-71021-1 024 7 $a10.1007/978-3-030-71021-7 035 $a(CKB)4100000011918709 035 $a(DE-He213)978-3-030-71021-7 035 $a(MiAaPQ)EBC6606063 035 $a(Au-PeEL)EBL6606063 035 $a(OCoLC)1250014969 035 $a(PPN)255882149 035 $a(EXLCZ)994100000011918709 100 $a20220114d2021 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn undergraduate primer in algebraic geometry /$fCiro Ciliberto 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (XI, 327 p. 1 illus.) 225 1 $aUnitext ;$vVolume 129 311 $a3-030-71020-3 320 $aIncludes bibliographical references and index. 327 $a1 Affine and projective algebraic sets -- 2 Basic notions of elimination theory and applications -- 3 Zariski closed subsets and ideals in the polynomials ring -- 4 Some topological properties -- 5 Regular and rational functions -- 6 Morphisms -- 7 Rational maps -- 8 Product of varieties -- 9 More on elimination theory -- 10 Finite morphisms -- 11 Dimension -- 12 The Cayley form -- 13 Grassmannians -- 14 Smooth and singular points -- 15 Power series -- 16 A ne plane curves -- 17 Projective plane curves -- 18 Resolution of singularities of curves -- 19 Divisors, linear equivalence, linear series -- 20 The Riemann-Roch Theorem. 330 $aThis book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann?Roch and Riemann?Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point?set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter. 410 0$aUnitext ;$vVolume 129. 606 $aGeometry, Algebraic 606 $aGeometria algebraica$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Algebraic. 615 7$aGeometria algebraica 676 $a516.35 700 $aCiliberto$b C$g(Ciro),$f1950-$042512 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466407703316 996 $aAn Undergraduate Primer in Algebraic Geometry$91972316 997 $aUNISA