# IJPAM: Volume 23, No. 2 (2005)

**ON THE MINIMAL FREE RESOLUTION**

OF GENERAL UNIONS IN OF

A FINITE FIX SUBSET AND

MANY GENERAL POINTS

OF GENERAL UNIONS IN OF

A FINITE FIX SUBSET AND

MANY GENERAL POINTS

Department of Mathematics

University of Trento

380 50 Povo (Trento) - Via Sommarive, 14, ITALY

e-mail: ballico@science.unitn.it

**Abstract.**Let
be a finite subset such that no three points of are
collinear. Set
and
. Fix an integer such that
,
i.e. assume that the first integer such that
satisfies . Let
be a general subset such that . Here we prove that the minimal free resolution of is the expected one, i.e.
for all ,
for all and the homogeneous ideal
of is minimally generated by
forms of degree and
forms
of degree .

**Received: **August 3, 2005

**AMS Subject Classification: **14N05

**Key Words and Phrases: **minimal free resolution, zero-dimensional scheme, postulation, fat point, double point

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2005

**Volume:** 23

**Issue:** 2