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View - Departament de Matemàtica Aplicada II - UPC

J.M. Miret et al. / Journal of Symbolic Computation 44 (2009) 1425–1447 1441

# It has dimension 8 and its generating classes are b, m, p and z

# (the later corresponds to the tautological "hyperplane" class)

PZ=variety(8, {gcs=[b,m,p,z]});

# The table of monomial values of PZ is computed as follows:

PZ(monomial_values)=

{ m^i*b^j*p^h*z^(8-i-j-h) ->

integral(m^i*b^j*p^h*segre(7-i-j-h,Dquot),PP)

with (i,j,h) in (0..3,0..min(3,5-i),0..(7-i-j))};

# Udz is the bundle Ud lifted to PZ

Udz=sheaf(3,[m,m^2,m^3],PZ);

# Enodz is Qqp twisted by 2m-p direct sum the third symmetric

# power of Qdp

Enodz=Udz * o_(2*m-p,PZ) + o_(m-z+2*p-2*b,PZ);

# Dnodz is Enodz twisted by -3m

Dnodz= Enodz * o_(-3*m,PZ);

# The table of monomial values of Knodz is computed as follows:

Knodz(monomial_values)=

{ m^i*b^j*p^h*z^k*n^(11-i-j-h-k) ->

integral(m^i*b^j*p^h*z^k*segre(8-i-j-h-k,Enodz),PZ)

with (i,j,h,k) in (0..3,0..min(3,5-i),0..(7-i-j),0..(8-i-j-h)) };

#tabulate(Knodz(monomial_values),"Knodz.res");

4.3. Intersection numbers on K z,s

nod

# PZ is a projective bundle of planes over PP

# It has dimension 8 and its generating classes are b, m, p and z

# Ud2 is the bundle Ud lifted to PZ

Ud2=sheaf(3,[m,m^2,m^3],PZ);

# Eg is Ud2 twisted by 2m-p

Eg=Ud2 * o_(2*m-p,PZ);

# Egg is Eg twisted by -3m

Egg= Eg * o_(-3*m,PZ);

# Pg is a projective bundle of planes over PZ # It has dimension 10

and its generating classes are b, m, p, z and g # the later

corresponds to the tautological # "hyperplane" class of the bundle

Pg=variety(10, {gcs=[b,m,p,z,g]});

# The table of monomial values of Pg is computed as follows:

Pg(monomial_values)=

{ m^i*b^j*p^h*z^k*g^(10-i-j-h-k) ->

integral(m^i*b^j*p^h*z^k*segre(8-i-j-h-k,Egg),PZ)

with (i,j,h,k) in (0..3,0..min(3,5-i),0..(7-i-j),0..(8-i-j-h)) };

# Enods is a direct sum of two line bundles