Displaying similar documents to “Infinite-dimensional complex projective spaces and complete intersections”

Lelong numbers on projective varieties

Rodrigo Parra (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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Given a positive closed (1,1)-current T defined on the regular locus of a projective variety X with bounded mass near the singular part of X and Y an irreducible algebraic subset of X , we present uniform estimates for the locus inside Y where the Lelong numbers of T are larger than the generic Lelong number of T along Y .

Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

William W. Adams, Philippe Loustaunau, Victor P. Palamodov, Daniele C. Struppa (1997)

Annales de l'institut Fourier

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In this paper we prove that the projective dimension of ℳ n = R 4 / ⟨ A n ⟩ is 2 n - 1 , where R is the ring of polynomials in 4 n variables with complex coefficients, and ⟨ A n ⟩ is the module generated by the columns of a 4 × 4 n matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of n quaternionic variables. As a corollary we show that the sheaf ℛ of regular functions has flabby dimension 2 n - 1 , and we prove a cohomology vanishing theorem...

Approximation of C ∞ -functions without changing their zero-set

F. Broglia, A. Tognoli (1989)

Annales de l'institut Fourier

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For a C ∞ function ϕ : M → ℝ (where M is a real algebraic manifold) the following problem is studied. If ϕ - 1 ( 0 ) is an algebraic subvariety of M , can ϕ be approximated by rational regular functions f such that f - 1 ( 0 ) = ϕ - 1 ( 0 ) ? We find that this is possible if and only if there exists a rational regular function g : M → ℝ such that g - 1 ( 0 ) = ϕ - 1 ( 0 ) and g(x) · ϕ ( x ) ≥ 0 for any x in ℝ n . Similar results are obtained also in the analytic and in the Nash cases. For non approximable functions the minimal flatness locus...

The trivial locus of an analytic map germ

H. Hauser, G. Muller (1989)

Annales de l'institut Fourier

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We prove: For a local analytic family { X s } s ∈ S of analytic space germs there is a largest subspace T in S such that the family is trivial over T . Moreover the reduction of T equals the germ of those points s in S for which X s is isomorphic to the special fibre X 0 .

On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

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Here we give several examples of projective degenerations of subvarieties of ℙ t . The more important case considered here is the d-ple Veronese embedding of ℙ n ; we will show how to degenerate it to the union of d n n-dimensional linear subspaces of ℙ t ; t : = ( n + d ) / ( n ! d ! ) - 1 and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to...