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D.15.16.3 BettiNumsH

Procedure from library goettsche.lib (see goettsche_lib).

Usage:
BettiNumsH(n, b); n integer, b list of non-negative integers

Return:
list of non-negative integers

Purpose:
computes the Betti numbers of the Hilbert scheme
of n points on a surface with Betti numbers b

Note:
an empty list is returned if n<0 or b is not a list of non-negative integers or if there are not enough Betti numbers

Example:
 
LIB "goettsche.lib";
ring r=0, (z), ls;
// consider the projective plane P_2 with Betti numbers 1,0,1,0,1
list b=1,0,1,0,1;
// get the Betti numbers of the Hilbert scheme of 3 points on P_2
print( BettiNumsH(3, b) );
==> [1]:
==>    1
==> [2]:
==>    0
==> [3]:
==>    2
==> [4]:
==>    0
==> [5]:
==>    5
==> [6]:
==>    0
==> [7]:
==>    6
==> [8]:
==>    0
==> [9]:
==>    5
==> [10]:
==>    0
==> [11]:
==>    2
==> [12]:
==>    0
==> [13]:
==>    1