Projection on Segre varieties and determination of holomorphic mappings between real submanifolds

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.Comment: 16 page

Proper Actions of Lie Groups of Dimension n2 + 1 on n-Dimensional Complex Manifolds

In this paper, we continue to study actions of high-dimensional Lie groups on complex manifolds. We give a complete explicit description of all pairs (M,G), where M is a connected complex manifold of dimension n ≥ 2 and G is a connected Lie group of di

Effective actions of the unitary group on complex manifolds

We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of ℂn by its automorphism group

ASSOCIATED FORMS OF BINARY QUARTICS AND TERNARY CUBICS

Let (Formula presented.) be the vector space of forms of degree d ≥ 3 on ℂn, with n ≥ 2. The object of our study is the map Φ, introduced in earlier articles by M. Eastwood and the first two authors, that assigns every nondegenerate form in (Formula presented.) the so-called associated form, which is an element of (Formula presented.). We focus on two cases: those of binary quartics (n = 2, d = 4) and ternary cubics (n = 3, d = 3). In these situations the map Φ induces a rational equivariant involution on the projective space ℙ(Formula presented.), which is in fact the only nontrivial rational equivariant involution on ℙ(Formula presented.). In particular, there exists an equivariant involution on the space of elliptic curves with nonvanishing j-invariant. In the present paper, we give a simple interpretation of this involution in terms of projective duality. Furthermore, we express it via classical contravariants