330 KB518 KB184 KB2000Forstnerič, FrancPrezelj-Perman, Jasna87 f., 30 cm88 straniCOBISSID:9997657URN:URN:NBN:SI:doc-5GBRHESDslJ. Prezeljvisokošolska delaDisertacijeholomorfna submerzijaholomorfna vložitevholomorfni prerezhomotopski principikompleksna analizakompleksni prostorSteinov prostortangentni prostorHomotopski princip za submerzije s sprayem nad Steinovimi prostori| doktorska disertacija|The first part contains a proof of the homotopy principle for holomorphic submersions with sprays: "Let ?$Z$? be a complex space, ?$X$? Stein space, ?$h: Z \to Z$? surjective holomorphic submersion which locally admits a spray, ?$P$? a compact Hausdorff space and ?$a_p: X \to Z$?, ?$p \in P$?, a continuous family of continuous sections of submersion ?$h: Z \to X$?. Then there exist a continuous family of continuous sections ?$a_{p,t}: X \to Z$?, ?$p \in P$?, ?$t \in 0,1$?, of ?$h: Z \to X$?, such that ?$a_{p,0} = a_p$?, ?$p \in P$? and the section ?$a_{p,1}: X \to Z$? is holomorphic for each ?$p \in P$?." The second part is an embedding theorem for Stein manifolds with interpolation on discrete sets. "Let ?$X$? be an ?$n$?-dimensional Stein manifold, ?$Y \subset X$? a discrete subset and ?$\varphi: Y \to \Cc^{n+q}$? a proper injective map. If ?$n=1$? and ?$q \ge 2$? or ?$n>1$? and ?$q \ge \max \left{ \left \frac{n+1}{2} \right + 1,3 \right}$? then there exist a proper holomorphic enbedding ?$\Phi: X \to \Cc^{n+q}$? extending ?$\varphi$?."V prvem delu je dokazan homotopski princip za submerzije s sprayi: "Naj bo ?$Z$? kompleksen prostor, ?$X$? Steinov prostor, ?$h: Z \to Z$? surjektivna holomorfna submerzija, ki lokalno dopušča spray, ?$P$? kompakten Hausdorffov prostor in ?$a_p: X \to Z$?, ?$p \in P$?, zvezna družina zveznih prerezov submerzije ?$h: Z \to X$?. Potem obstaja taka zvezna družina zveznih prerezov ?$a_{p,t}: X \to Z$?, ?$p \in P$?, ?$t \in 0,1$?, da je ?$a_{p,0} = a_p$?, ?$p \in P$? in je za vsak ?$p \in P$? prerez ?$a_{p,1}: X \to Z$? holomorfen." Glavni izrek v drugem delu je vložitveni izrek za Steinove mnogoterosti z interpolacijo na diskretnih množicah. "Naj bo ?$X$? ?$n$?-dimenzionalna Steinova mnogoterost, ?$Y \subset X$? diskretna podmnožica in ?$\varphi: Y \to \Cc^{n+q}$? prava injekcija. Če je ?$n=1$? in ?$q \ge 2$? ali ?$n>1$?in ?$q \ge \max \left{ \left \frac{n+1}{2} \right + 1,3\right}$?, obstaja pravaholomorfna vložitwv ?$\Phi: X \to \Cc^{n+q}$?, ki razširi ?$\varphi$?."doktorska disertacijaTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Fakulteta za matematiko in fiziko