Hermitian variety Totally Explained

Everything about Hermitian Variety totally explained

Hermitian varieties are in a sense a generalisation of quadrics, and occur naturally in the theory of polarities.

Definition

Let K be a field with an involutive automorphism

heta

. Let n be an integer

geq 1

and V be an(n+1)-dimensional vectorspace over K.
A Hermitian variety H in PG(V) is a set of points of which the representing vectorlines consist of isotropic points of a nontrivial sesquilinear form on V.

Representation

Let

e_0,e_1,ldots,e_n

be a basis of V. If a point p in the projective space has homogenous coordinates

(X_0,ldots,X_n)

with respect to this basis, it's on the Hermitian variety if and only if :

sum_.

Tangent spaces and singularity

Let p be a point on the Hermitian variety H. A line L through p is by definion tangent when it's contains only one point (p itself) of the variety or lies completely on the variety. One can prove that these lines form a subspace, either a hyperplane of the full space. In the latter case, the point is singular.

Further Information

Get more info on 'Hermitian Variety'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://hermitian_variety.totallyexplained.com">Hermitian variety Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.