TY - JOUR
T1 - Hermitian symmetric polynomials and CR complexity
AU - D'Angelo, John P.
AU - Lebl, Jiří
N1 - Acknowledgements The authors acknowledge support from NSF grants DMS 07-53978 (JPD) and DMS 09-00885 (JL). They also wish to thank AIM for the workshop on CR Complexity Theory in 2006 which helped nourish some of these ideas.
PY - 2011/7
Y1 - 2011/7
N2 - Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms.We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.
AB - Properties of Hermitian forms are used to investigate several natural questions from CR geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms.We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.
KW - CR complexity theory
KW - Embeddings of CR manifolds
KW - Hermitian forms
KW - Hyperquadrics Signature pairs
KW - Proper holomorphic mappings
UR - https://www.scopus.com/pages/publications/80051783178
UR - https://www.scopus.com/pages/publications/80051783178#tab=citedBy
U2 - 10.1007/s12220-010-9160-1
DO - 10.1007/s12220-010-9160-1
M3 - Article
AN - SCOPUS:80051783178
SN - 1050-6926
VL - 21
SP - 599
EP - 619
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -