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isRegularMap -- whether a map to projective space is regular

Description

This function runs baseLocusOfMap(f) and checks whether the ideal defining the base locus is the whole ring.

i1 : P5 = QQ[a..f];
i2 : P2 = QQ[x,y,z];
i3 : M = matrix{{a,b,c},{d,e,f}};

              2       3
o3 : Matrix P5  <-- P5
i4 : blowUpSubvar = P5/(minors(2, M) + ideal(b - d));
i5 : f = map(blowUpSubvar, P2, {a, b, c});

o5 : RingMap blowUpSubvar <-- P2
i6 : isRegularMap(f)

o6 = true

Ways to use isRegularMap:

  • isRegularMap(RationalMapping)
  • isRegularMap(RingMap)

For the programmer

The object isRegularMap is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/RationalMaps.m2:2194:0.