LDR 02508 a2200301 4500 010 _a9781107602724 _bbr. 090 _a16215 101 _aeng 102 _aGB 100 _a20170920 frey50 200 _bM _a3264 and all that _fDavid Eisenbud, Joe Harris _ea second course in algebraic geometry 210 _cCambridge University Press _aCambridge _dcop. 2016 215 _a1 vol. (xiv-616 p.) _cfig., couv. ill. en coul. _d26 300 _aPublisher’s description: This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles’ nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré’s development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics 320 _aBibliogr. p. [594]-601. Index 676 _a2010 686 _20 _9161935 _a14-01 _bAlgebraic geometry _xInstructional exposition (textbooks, tutorial papers, etc.) 686 _20 _9162102 _a14N10 _bAlgebraic geometry -- Projective and enumerative geometry _xEnumerative problems (combinatorial problems) 686 _20 _9161960 _a14C17 _bAlgebraic geometry -- Cycles and subschemes _xIntersection theory, characteristic classes, intersection multiplicities 686 _20 _9161959 _a14C15 _bAlgebraic geometry -- Cycles and subschemes _x(Equivariant) Chow groups and rings; motives 700 _4070 _9173186 _aEisenbud _bDavid _f1947- 701 _4070 _9173053 _aHarris _bJoe _f1951- 856 _uhttp://www.ams.org/mathscinet-getitem?mr=3617981 _zMSN 856 _uhttps://zbmath.org/?q=an:1341.14001 _zzbMath 905 _aaw _b2017 906 _aaw _b2017-09-29 001 16215 995 _f12410-01 _xachat Ebsco _918508 _cCMI _20 _k14 EIS _o0 _eSalle R _z32 _bCMI