# Questions tagged [pfaffian]

Every question that is related to the Pfaffian polynomial and its traits.

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### Local meaning of the Pfaffian of the curvature

The Ricci and scalar curvatures have very nice pointwise interpretations (using the local expression for the volume form for example). So, (at least Ricci) having special metrics (like Einstein) can ...
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### Rational map given by pfaffians

Consider a general skew-symmetric $(n+1)\times (n+1)$ matrix $Z$, and let su map $Z$ to the point of $\mathbb{P}^n$ determined by $[pf_0(Z):\dots:pf_n(Z)]$ where the $pf_i(Z)$ are the principal ...
405 views

### Pfaffian representation of the Fermat quintic

It is known (see for instance Beauville - Determinantal hypersurfaces) that a generic homogeneous polynomial in $5$ variables of degree $5$ with complex coefficients can be written as the Pfaffian of ...
616 views

### Determinant is to Pfaffian as resultant is to what?

This is an irresponsible question: I do not have done any thinking on it, or even literature search. I just became curious whether there is some modification of the notion of a common root of two ...
370 views

### Detailed modern references for basic properties of Pfaffians over commutative rings

Pfaffians are important to algebraic combinatorics, at least. This is to propose the making of a 'wiki' list, more modern, precise and compressed than e.g. the relevant Wikipedia page (nothing ...
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### the pfaffian-adjugate and its counterparts for matrices odd size

Let $R$ be a commutative ring (zero characteristic). Take a skew-symmetric matrix $A\in Mat^{skew-sym}(n,R)$. If $n$ is even, then $\det(A)=Pf^2(A)$ and there exists the "Pfaffian adjugate/adjoint" ...
362 views

### Singularities of Pfaffian hypersurfaces

Let $X\subset\mathbb{P}^4$ be an hypersurface of degree six given by the Pfaffian of a $6\times 6$ matrix $M$ whose entries are quadratic forms in the homogeneous coordinates of $\mathbb{P}^4$. I am ...