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# baseLocus -- the base locus of a multi-rational map

## Synopsis

• Usage:
baseLocus Phi
• Inputs:
• Phi,
• Outputs:
• , the base locus of Phi, that is, the locus where it is not defined

## Description

 i1 : t = gens ring PP_(ZZ/33331)^5; i2 : Phi = rationalMap {rationalMap {t_0,t_1,t_2},rationalMap {t_3,t_4,t_5}}; o2 : MultirationalMap (rational map from PP^5 to PP^2 x PP^2) i3 : X = baseLocus Phi; o3 : ProjectiveVariety, surface in PP^5 i4 : describe X o4 = ambient:.............. PP^5 dim:.................. 2 codim:................ 3 degree:............... 2 generators:........... 2^9 purity:............... true dim sing. l.:......... -1 i5 : Psi = inverse(Phi|random(3,baseLocus Phi)); o5 : MultirationalMap (birational map from PP^2 x PP^2 to hypersurface in PP^5) i6 : Y = baseLocus Psi; o6 : ProjectiveVariety, surface in PP^2 x PP^2 i7 : describe Y o7 = ambient:.............. PP^2 x PP^2 dim:.................. 2 codim:................ 2 degree:............... 14 multidegree:.......... 2*T_0^2+5*T_0*T_1+2*T_1^2 generators:........... (1,2)^1 (2,1)^1 purity:............... true dim sing. l.:......... -1 Segre embedding:...... map to PP^8