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An example where it does not is given by the isolated singularity of x 2 + y 3 z + z 3 = 0 at the origin. Blowing it up gives the singularity x 2 + y 2 z + yz 3 = 0. It is not immediately obvious that this new singularity is better, as both singularities have multiplicity 2 and are given by the sum of monomials of degrees 2, 3, and 4.
One of the easiest examples to check of a Calabi-Yau manifold is given by the Fermat quintic threefold, which is defined by the vanishing locus of the polynomial = + + + + Computing the partial derivatives of gives the four polynomials = = = = = Since the only points where they vanish is given by the coordinate axes in , the vanishing locus is empty since [::::] is not a point in .
A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate "X" shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
The pinch point and the fold singularity are the only stable local singularities of maps from R 2 to R 3. It is named after the American mathematician Hassler Whitney . In string theory , a Whitney brane is a D7-brane wrapping a variety whose singularities are locally modeled by the Whitney umbrella.
Suppose that Y is a normal variety such that its canonical class K Y is Q-Cartier, and let f:X→Y be a resolution of the singularities of Y.Then = + where the sum is over the irreducible exceptional divisors, and the a i are rational numbers, called the discrepancies.