LEADER 03910nam 22005895 450 001 9910300106903321 005 20200629162037.0 010 $a4-431-56837-9 024 7 $a10.1007/978-4-431-56837-7 035 $a(CKB)4100000006674865 035 $a(DE-He213)978-4-431-56837-7 035 $a(MiAaPQ)EBC6315423 035 $a(PPN)230536905 035 $a(EXLCZ)994100000006674865 100 $a20180921d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Singularities /$fby Shihoko Ishii 205 $a2nd ed. 2018. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2018. 215 $a1 online resource (X, 236 p. 4 illus.) 311 $a4-431-56836-0 327 $a1. Sheaves, algebraic varieties and analytic spaces -- 2. Homological algebra and duality -- 3. Singularities, algebraization and resolutions of singularities -- 4. Divisors on a variety and the corresponding sheaves -- 5. Differential forms around the singularities -- 6. Two dimensional singularities -- 7. Higher dimensional singularities -- 8. Deformations of singularities. 330 $aThis book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have originated in the seventeenth century with the famous workDiscours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians? works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter. 606 $aGeometry, Algebraic 606 $aAssociative rings 606 $aRings (Algebra) 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 615 0$aGeometry, Algebraic. 615 0$aAssociative rings. 615 0$aRings (Algebra) 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aAlgebraic Geometry. 615 24$aAssociative Rings and Algebras. 615 24$aCommutative Rings and Algebras. 676 $a516.35 700 $aIshii$b Shihoko$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721189 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300106903321 996 $aTokui-ten no sh?kai$92554226 997 $aUNINA