Genus of Singular Varieties
The definition of geometric genus is carried over classically to singular curves C, by decreeing that
- pg(C)
is the geometric genus of the normalization C′. That is, since the mapping
- C′ → C
is birational, the definition is extended by birational invariance.
Read more about this topic: Geometric Genus
Famous quotes containing the words genus, singular and/or varieties:
“Methinks it would be some advantage to philosophy if men were named merely in the gross, as they are known. It would be necessary only to know the genus and perhaps the race or variety, to know the individual. We are not prepared to believe that every private soldier in a Roman army had a name of his own,—because we have not supposed that he had a character of his own.”
—Henry David Thoreau (1817–1862)
“It is singular how soon we lose the impression of what ceases to be constantly before us. A year impairs, a lustre obliterates. There is little distinct left without an effort of memory, then indeed the lights are rekindled for a moment—but who can be sure that the Imagination is not the torch-bearer?”
—George Gordon Noel Byron (1788–1824)
“Now there are varieties of gifts, but the same Spirit; and there are varieties of services, but the same Lord; and there are varieties of activities, but it is the same God who activates all of them in everyone.”
—Bible: New Testament, 1 Corinthians 12:4-6.