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Background

Part of the Progress in Mathematics book series (PM, volume 264)

Abstract

Throughout this book, ℙn will be the n-dimensional projective space over an algebraically closed field K of characteristic zero, \( R = K\left[ {x_0 ,x_1 , \ldots ,x_n } \right] \) and \( m = \left[ {x_0 ,x_1 , \ldots ,x_n } \right] \) its homogeneous maximal ideal. If M is a graded R-module, we distinguish two types of duals of M: the R-dual M*:= Hom R (M, R) and the K-dual MV:= HomK (M, K). A scheme V ⊂ ℙn will mean an equidimensional locally Cohen-Macaulay closed subscheme of ℙn. For a subscheme V of ℙn we denote by I V its ideal sheaf, \( I\left( V \right) = H_ * ^0 \left( {\mathcal{I}_V } \right): = \oplus _{t \in \mathbb{Z}} H^0 \left( {\mathbb{P}^n ,\mathcal{I}_V \left( t \right)} \right) \) its saturated homogeneous ideal (unless \( V = \not 0 \), in which case we let I(V) = m), A(V) = R/I(V) the homogeneous coordinate ring, and N v = Hom(I V , O V )the normal sheaf of V.

Keywords

Complete Intersection Hilbert Function Homogeneous Matrix Hilbert Polynomial Minimal Free Resolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

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