Local polynomial convexity of the union of two totallyreal surfaces at their intersection
 Sushil Gorai
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We consider the following question: Let S _{1} and S _{2} be two smooth, totallyreal surfaces in \({\mathbb{C}^2}\) that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is \({S_1\cup S_2}\) locally polynomially convex at the origin? If T _{0} S _{1} ∩ T _{0} S _{2} = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When \({dim_\mathbb{R}(T_0S_1\cap T_0S_2)=1}\) , we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.
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 Title
 Local polynomial convexity of the union of two totallyreal surfaces at their intersection
 Journal

Manuscripta Mathematica
Volume 135, Issue 12 , pp 4362
 Cover Date
 20110501
 DOI
 10.1007/s002290100405x
 Print ISSN
 00252611
 Online ISSN
 14321785
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Primary: 32E20
 46J10
 Authors

 Sushil Gorai ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India