LEADER 03583nam  22005535  450 
001 9910254062703321
005 20200705030811.0
010   $a3-319-32315-6
024 7 $a10.1007/978-3-319-32315-2
035   $a(CKB)3710000000749189
035   $a(DE-He213)978-3-319-32315-2
035   $a(MiAaPQ)EBC4591914
035   $a(PPN)194516296
035   $a(EXLCZ)993710000000749189
100   $a20160712d2016      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aHyperbolicity of Projective Hypersurfaces /$fby Simone Diverio, Erwan Rousseau
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XIV, 89 p. 3 illus.) 
225 1 $aIMPA Monographs ;$v5
311   $a3-319-32314-8 
320   $aIncludes bibliographical references.
327   $a- Introduction -- Kobayashi hyperbolicity: basic theory -- Algebraic hyperbolicity -- Jets spaces -- Hyperbolicity and negativity of the curvature -- Hyperbolicity of generic surfaces in projective 3-space -- Algebraic degeneracy for projective hypersurfaces.
330   $aThis book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these research fields (e.g. existence of Zariski dense entire curves should correspond to the (potential) density of rational points). Perhaps one of the conjectures which generated most activity in Kobayashi hyperbolicity theory is the one formed by Kobayashi himself in 1970 which predicts that a very general projective hypersurface of degree large enough does not contain any (non-constant) entire curves. Since the seminal work of Green and Griffiths in 1979, later refined by J.-P. Demailly, J. Noguchi, Y.-T. Siu and others, it became clear that a possible general strategy to attack this problem was to look at particular algebraic differential equations (jet differentials) that every entire curve must satisfy. This has led to some several spectacular results. Describing the state of the art around this conjecture is the main goal of this work.
410  0$aIMPA Monographs ;$v5
606   $aGeometry, Differential
606   $aGeometry, Algebraic
606   $aFunctions of complex variables
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
606   $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198
615  0$aGeometry, Differential.
615  0$aGeometry, Algebraic.
615  0$aFunctions of complex variables.
615 14$aDifferential Geometry.
615 24$aAlgebraic Geometry.
615 24$aSeveral Complex Variables and Analytic Spaces.
676   $a516.36
700   $aDiverio$b Simone$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755938
702   $aRousseau$b Erwan$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910254062703321
996   $aHyperbolicity of Projective Hypersurfaces$91963837
997   $aUNINA