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Rigidity of local holomorphic maps between Hermitian symmetric spaces
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Fang, Hanlong. Rigidity of local holomorphic maps between Hermitian symmetric spaces. Retrieved from https://doi.org/doi:10.7282/T3JM2F29

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TitleRigidity of local holomorphic maps between Hermitian symmetric spaces
NameFang, Hanlong (author); Huang, Xiaojun (chair); Song, Jian (internal member); Chanillo, Sagun (internal member); Berhanu, Shiferaw (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-05 (degree)
SubjectMathematics, Rigidity (Geometry)
Extent1 online resource (vii, 102 p.)
DescriptionIn this dessertaion, rigidity of local holomorphic maps between Hermitian symmet ric spaces has been studied. For local holomorphic maps from an irreducible Hermi tian symmetric spaces of compact type to itself, which is equipped with a canonical K¨ahler-Eisntein metric, we show that every map extends to an isometry of the mani fold, provided that the maps satisfy a measure-preserving equation and are generically non-degenerate. To establish the rigidity result, a notion of Serge variety and Segre family in the algebraic setting is introduced. Before obtaining the main theorem, we first prove a basic property for partially degenerate holomorphic maps in a general set ting. Then we establish the Nash-algebraicity for one of these maps by applying this basic property. Here the explicit expression of the mimimal embedding of the manifold into a certain projective space is essentially used. Standard monodormy argument is then applied to show the rationality for this Nash-algebraic map. Lastly by a covering trick we show that the map is a birational map and further an isometry. Hence by induction, we conclude the main theorem. This thesis is based on a joint work with Xiaojun Huang and Ming Xiao ( [FHX])
NotePh.D.
NoteIncludes bibliographical references
Noteby Hanlong Fang
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3JM2F29
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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