TY - BOOK ID - 4793834 TI - Lectures on algebraic geometry. PY - 2011 SN - 1283369656 9786613369659 3834883301 3834818445 PB - Wiesbaden : Vieweg+Teubner, DB - UniCat KW - Geometry, Algebraic. KW - Sheaf theory. KW - Riemann surfaces. KW - Surfaces, Riemann KW - Functions KW - Cohomology, Sheaf KW - Sheaf cohomology KW - Sheaves, Theory of KW - Sheaves (Algebraic topology) KW - Algebraic topology KW - Algebraic geometry KW - Geometry KW - Geometry. KW - Algebra. KW - Mathematics KW - Mathematical analysis KW - Euclid's Elements UR - https://www.unicat.be/uniCat?func=search&query=sysid:4793834 AB - This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them. ER -