LEADER 04748nam 22009375 450 001 9910154747503321 005 20190708092533.0 010 $a1-4008-8206-0 024 7 $a10.1515/9781400882069 035 $a(CKB)3710000000627309 035 $a(MiAaPQ)EBC4738664 035 $a(DE-B1597)467993 035 $a(OCoLC)979759957 035 $a(DE-B1597)9781400882069 035 $a(EXLCZ)993710000000627309 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aLectures on Curves on an Algebraic Surface. (AM-59), Volume 59 /$fDavid Mumford 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1966 215 $a1 online resource (221 pages) 225 0 $aAnnals of Mathematics Studies ;$v332 311 $a0-691-07993-5 320 $aBibliography. 327 $tFrontmatter -- $tINTRODUCTION -- $tCONTENTS -- $tLECTURE 1. RAW MATERIAL ON CURVES ON SURFACES, AND THE PROBLEMS SUGGESTED -- $tLECTURE 2. THE FUNDAMENTAL EXISTENCE PROBLEM AND TWO ANALYTIC PROOFS -- $tLECTURE 3. PRE-SCHEMES AND THEIR ASSOCIATED "FUNCTOR OF POINTS" -- $tLECTURE 4. USES OF THE FUNCTOR OF POINTS -- $tAPPENDIX TO LECTURE 4. RE REPRESENTABLE FUNCTORS AND ZARISKI TANGENT SPACES -- $tLECTURE 5. Pro j AND INVERTIBLE SHEAVES -- $tAPPENDIX TO LECTURE 5 -- $tLECTURE 6. PROPERTIES OP MORPHISMS AND SHEAVES -- $tLECTURE 7. RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON Pn -- $tLECTURE 8. FLATTENING STRATIFICATIONS -- $tLECTURE 9. CARTIER DIVISORS -- $tLECTURE 10. FUNCTORIAL PROPERTIES OF EFFECTIVE CARTIER DIVISORS -- $tLECTURE 11. BACK TO THE CLASSICAL CASE -- $tLECTURE 12. THE OVER-ALL CLASSIFICATION OF CURVES ON SURFACES -- $tLECTURE 13. LINEAR SYSTEMS AND EXAMPLES -- $tLECTURE 14. SOME VANISHING THEOREMS -- $tLECTURE 15. UNIVERSAL FAMILIES OF CURVES -- $tLECTURE 16. THE METHOD OF CHOW SCHEMES -- $tLECTURE 17. GOOD CURVES -- $tLECTURE 18. THE INDEX THEOREM -- $tLECTURE 19. THE PICARD SCHEME : OUTLINE -- $tLECTURE 20. INDEPENDENT 0-CYCLES ON A SURFACE -- $tLECTURE 21. THE PICARD SCHEME: CONCLUSION -- $tLECTURE 22. THE CHARACTERISTIC MAP OP A FAMILY OP CURVES -- $tLECTURE 23. THE FUNDAMENTAL THEOREM VIA KODAIRA-SPENCER -- $tLECTURE 24. THE STRUCTURE OF ? -- $tLECTURE 25. THE FUNDAMENTAL THEOREM VIA GROTHENDIECK-CARTIER -- $tLECTURE 26. RING SCHEMES; THE WITT SCHEME -- $tAPPENDICES TO LECTURE 26 APPENDICES TO LECTURE 26 -- $tLECTURE 27. THE FUNDAMENTAL THEOREM IN CHARACTERISTIC p -- $tWORKS REFERRED TO -- $tBackmatter 330 $aThese lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint. 410 0$aAnnals of mathematics studies ;$vno. 59. 606 $aCurves, Algebraic 606 $aSurfaces, Algebraic 610 $aAffine space. 610 $aAlgebraic geometry. 610 $aAlgebraic topology. 610 $aAlgebraically closed field. 610 $aBinary operation. 610 $aChern class. 610 $aCoherent sheaf. 610 $aCohomology. 610 $aComplex vector bundle. 610 $aDense set. 610 $aDifferential form. 610 $aDirect product. 610 $aFamily of curves. 610 $aFormal power series. 610 $aFunctor. 610 $aGeneric point. 610 $aGroup ring. 610 $aHomomorphism. 610 $aInvertible sheaf. 610 $aLocal ring. 610 $aMorphism of schemes. 610 $aMorphism. 610 $aNonlinear system. 610 $aOpen set. 610 $aPairwise. 610 $aPolynomial. 610 $aPower series. 610 $aProjective space. 610 $aRational function. 610 $aRational point. 610 $aSheaf (mathematics). 610 $aSubring. 610 $aSummation. 610 $aSymmetric function. 610 $aTopology. 610 $aUnion (set theory). 610 $aZariski topology. 610 $aZero divisor. 615 0$aCurves, Algebraic. 615 0$aSurfaces, Algebraic. 676 $a516.5 700 $aMumford$b David, $042095 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154747503321 996 $aLectures on Curves on an Algebraic Surface. (AM-59), Volume 59$92788791 997 $aUNINA