1,721,001 research outputs found
When K+(n-4)L fails to be nef
No full textLet X be a smooth complex projective variety of dimension n and let L be an ample line bundle on X. We study polarized pairs (X,L) for which K+(n-3)L is nef but K+(n-4)L fails to be nef
Vector spaces of skew-symmetric matrices of constant rank
No full textWe study the orbits of vector spaces of skew-symmetric matrices of
constant rank 2r and type (N + 1) x (N + 1) under the natural action of
SL(N + 1), over an algebraically closed field of characteristic zero. We
give a complete description of the orbits for vector spaces of dimension
2, relating them to some 1-generic matrices of linear forms. We also
show that, for each rank two vector bundle on P^2 defining a triple
Veronese embedding of P^2 in G(1, 7), there exists a vector space of 8
x 8 skew-symmetric matrices of constant rank 6 whose kernel bundle is
the dual of the given rank two vector bundle
Evidence to subcanonicity of codimension two subvarieties of G(1,4)
No full textIn this paper, we show that any smooth subvariety of codimension two in
G(1,4) (the Grassmannian of lines of P-4) of degree at most 25 is
subcanonical. Analogously, we prove that smooth subvarieties of
codimension two in G(1,4) that are not of general type have degree <= 32
and we classify all of them. In both classifications, any subvariety in
the final list is either a complete intersection or the zero locus of a
section of a twist of the rank-two universal bundle on G(1,4)
On the Hilbert Scheme of Palatini threefolds
No full textIn this paper we study the Hilbert scheme of Palatini threefolds X in P-5. We prove that such a scheme has an irreducible component containing X which is birational to the Grassmannian G(3, P^14) and we determine the exceptional locus of the birational map
On the Hilbert scheme of varieties defined by maximal minors
No full textWe compute the dimension of the Hilbert scheme of subvarieties
of positive dimension in
projective space which are cut by maximal minors
of a matrix with polynomial entries
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