normal complex analytic variety
In particular, if is a complex analytic subvariety, it is normal at if and only if every weakly holomorphic function through extends to be holomorphic in a neighbourhood of in .
To see that this definition is equivalent to the usual one, that is, that is normal at if and only if (the ring of germs of holomorphic functions at ) is integrally closed, we need the following theorem. Let be the total quotient ring of , that is, the ring of germs of meromorphic functions.
Let be a local complex analytic variety. Then is the integral closure of in
- 1 Hassler Whitney. . Addison-Wesley, Philippines, 1972.
|Title||normal complex analytic variety|
|Date of creation||2013-03-22 17:41:48|
|Last modified on||2013-03-22 17:41:48|
|Last modified by||jirka (4157)|
|Synonym||normal analytic variety|
|Defines||normal complex analytic space|
|Defines||normal complex analytic subvariety|
|Defines||normal analytic space|
|Defines||normal analytic subvariety|