# On some properties of partial intersection schemes.

Collectanea Mathematica (2003)

• Volume: 54, Issue: 3, page 255-267
• ISSN: 0010-0757

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## Abstract

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Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other; in particular, in codimension 3 case we see that [(p+5)/2] ≤ m ≤ 2p+1 and each m and p satisfying the above inequality can be realized.

## How to cite

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Ragusa, Alfio, and Zappalà, Giuseppe. "On some properties of partial intersection schemes.." Collectanea Mathematica 54.3 (2003): 255-267. <http://eudml.org/doc/43100>.

@article{Ragusa2003,
abstract = {Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other; in particular, in codimension 3 case we see that [(p+5)/2] ≤ m ≤ 2p+1 and each m and p satisfying the above inequality can be realized.},
author = {Ragusa, Alfio, Zappalà, Giuseppe},
journal = {Collectanea Mathematica},
keywords = {Intersección; Esquemas; Función de Hilbert; Ligaduras Gorenstein; Hilbert function; Betti numbers; liaison; arithmetically Cohen-Macaulay scheme; partial intersection schemes},
language = {eng},
number = {3},
pages = {255-267},
title = {On some properties of partial intersection schemes.},
url = {http://eudml.org/doc/43100},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Ragusa, Alfio
AU - Zappalà, Giuseppe
TI - On some properties of partial intersection schemes.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 3
SP - 255
EP - 267
AB - Partial intersection subschemes of Pr of codimension c were used to furnish various graded Betti numbers which agree with a fixed Hilbert function. Here we study some further properties of such schemes; in particular, we show that they are not in general licci and we give a large class of them which are licci. Moreover, we show that all partial intersections are glicci. We also show that for partial intersections the first and the last Betti numbers, say m and p respectively, give bounds each other; in particular, in codimension 3 case we see that [(p+5)/2] ≤ m ≤ 2p+1 and each m and p satisfying the above inequality can be realized.
LA - eng
KW - Intersección; Esquemas; Función de Hilbert; Ligaduras Gorenstein; Hilbert function; Betti numbers; liaison; arithmetically Cohen-Macaulay scheme; partial intersection schemes
UR - http://eudml.org/doc/43100
ER -

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