Base Locus
For more details on this topic, see Base locus.If all divisors in the system share common points, this is referred to as the base locus of the linear system. Geometrically, this corresponds to the common intersection of the varieties. Linear systems may or may not have a base locus – for example, the pencil of affine lines has no common intersection, but given two (nondegenerate) conics in the complex projective plane, they intersect in four points (counting with multiplicity) and thus the pencil they define has these points as base locus.
Read more about this topic: Linear System Of Divisors
Famous quotes containing the words base and/or locus:
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Love can transpose to form and dignity.
Love looks not with the eyes, but with the mind,
And therefore is winged Cupid painted blind.”
—William Shakespeare (1564–1616)
“Seeing the locus of joy as the gate
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—Denise Levertov (b. 1923)