TY - BOOK ID - 7689814 TI - Lectures on algebraic geometry. PY - 2011 SN - 3834826863 3834804320 3834881597 PB - Wiesbaden : Vieweg, DB - UniCat KW - Algebra. KW - Geometry, Algebraic. KW - Mathematics. KW - Mathematics KW - Physical Sciences & Mathematics KW - Geometry KW - Algebraic topology. KW - Sheaf theory. KW - Riemann surfaces. KW - Surfaces, Riemann KW - Cohomology, Sheaf KW - Sheaf cohomology KW - Sheaves, Theory of KW - Sheaves (Algebraic topology) KW - Algebraic geometry KW - Algebraic geometry. KW - Algebraic Geometry. KW - Functions KW - Algebraic topology KW - Topology KW - Geometry, algebraic. KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:7689814 AB - In this second volume of "Lectures on Algebraic Geometry", the author starts with some foundational concepts in the theory of schemes and gives a somewhat casual introduction into commutative algebra. After that he proves the finiteness results for coherent cohomology and discusses important applications of these finiteness results. In the two last chapters, curves and their Jacobians are treated and some outlook into further directions of research is given. The first volume is not necessarily a prerequisite for the second volume if the reader accepts the concepts on sheaf cohomology. On the other hand, the concepts and results in the second volume have been historically inspired by the theory of Riemann surfaces. There is a deep connection between these two volumes, in spirit they form a unity. Basic concepts of the Theory of Schemes - Some Commutative Algebra - Projective Schemes - Curves and the Theorem of Riemann-Roch - The Picard functor for curves and Jacobians. Prof. Dr. Günter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany. ER -