000			01890 a2200193 4500
008			180331b c2004 xxu||||| |||| 00| 0 eng d
020			_a9780821835555
082			_a516.35 _bCUT
100			_aCutkosky, Steven Dale
245			_aResolution of singularities
260			_bAmerican Mathematical Society, _c2004. _aProvidence:
300			_avii, 186 p. ; _b27 cm.
365			_aINR _b3022.20
440			_aGraduate studies in mathematics; v. 63
500			_aIncludes bibliographical references and index.
520			_aThe notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic." "The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of D-modules, topology, and mathematical physics." "This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic.". "Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing insight and intuition for the novice (or expert). There are many examples and exercises throughout the text." "The book is suitable for a second course on a topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.
650			_aSingularities (Mathematics)
942			_2ddc _cTD
999			_c47370 _d47370