# Questions tagged [conic-bundles]

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3
questions

**6**

votes

**1**answer

520 views

### What is a conic bundle and why is it called so?

I am desperately trying to understand what is a conic bundle. It seems like this is a completely standard term in algebraic geometry, there is even a page on wiki about it, but this doesn't really ...

**1**

vote

**0**answers

38 views

### How explicitly write a projective transformation between the conics over the univariate function field?

Consider the quadratic forms
$$
Q_1 = x^2 + y^2 - (t^2+1)z^2,\qquad Q_2 = x^2 + y^2 - z^2
$$
over the rational function field $\mathbb{F}_p(t)$, where $p > 2$ is a prime such that $t^2 + 1$ is ...

**6**

votes

**0**answers

145 views

### Conic bundles which are rational but with non-rational generic fibres

Let $n\ge 1$ be an integer and let us work over the field of complex numbers. Let $\mathcal{R}_n$ denote the set of rational conic bundles $\pi\colon X\to \mathbb{P}^n$ (morphisms such that the ...