Data di Pubblicazione:
2015
Citazione:
Hilbert surfaces of bipolarized varieties / M.C. Beltrametti, A. Lanteri, M. Lavaggi. - In: REVUE ROUMAINE DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0035-3965. - 60:3(2015 Dec), pp. 281-319.
Abstract:
Let X be a normal Gorenstein complex projective variety. We introduce the
Hilbert variety VX associated to the Hilbert polynomial χ(x1L1; : : : ; xÞLÞ), where
L1; : : : ;LÞ is a basis of Pic(X), Þ being the Picard number of X, and x1; : : : ; xÞ
are complex variables. After reviewing general properties of VX, we focus on the
following specific topics. First, we consider the Hilbert surface of a bipolarized
variety (X;L1;L2), namely, the surface of degree dim(X) in a 3-dimensional
affine space, associated to χ(xKX + yL1 + zL2). Special emphasis is given to
the case of 3-folds. Next, we treat the case of the Hilbert curve of a polarized
4-fold (X;L), that is, the plane quartic curve associated to χ(xKX + yL). We
also study quotients of Hilbert surfaces under the Serre involution s induced by
Serre duality, and we characterize surfaces in a 3-dimensional affine space which
are invariant under s.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
multipolarized variety; Hilbert variety; bidegree; Serre involution
Elenco autori:
M.C. Beltrametti, A. Lanteri, M. Lavaggi
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