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Papers

The relative Hilbert scheme of projection morphisms

http://dx.doi.org/10.1142/S0218196716500077

AuthorHosung Kim
JournalInternational Journal of Algebra and Computation 26(1) (2016
Link http://dx.doi.org/10.1142/S0218196716500077
Classification of papersSCI

Let

Y

be a smooth hypersurface of degree

d

in a projective space

ℙ^{n}

and take a point

y

in

ℙ^{n} \ Y

. Let

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

be the relative Hilbert scheme parametrizing zero-dimensional subscheme, of length

m

, of fibers of the projection morphism

Y \to ℙ^{n - 1}

from

y

. In this paper we present an embedding of the relative Hilbert scheme

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

into a weighted projective space and describe its defining ideal for general

y

. We also study line bundles on the relative Hilbert scheme

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

for

n \geq 4

and general

y

$y$ ..

Let

Y

be a smooth hypersurface of degree

d

in a projective space

ℙ^{n}

and take a point

y

in

ℙ^{n} \ Y

. Let

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

be the relative Hilbert scheme parametrizing zero-dimensional subscheme, of length

m

, of fibers of the projection morphism

Y \to ℙ^{n - 1}

from

y

. In this paper we present an embedding of the relative Hilbert scheme

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

into a weighted projective space and describe its defining ideal for general

y

. We also study line bundles on the relative Hilbert scheme

{Hilb}_{y}^{[m]} (Y / ℙ^{n - 1})

for

n \geq 4

and general

y

$y$ ..