Structure fractals and para-quaternionic geometry

Julian Ławrynowicz; Massimo Vaccaro

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We construct new birational maps between quadrics over a field. The maps apply to several types of quadratic forms, including Pfister neighbors, neighbors of multiples of a Pfister form, and half-neighbors. One application is to determine which quadrics over a field are ruled (that is, birational to the projective line times some variety) in a larger range of dimensions. We describe ruledness completely for quadratic forms of odd dimension at most 17, even dimension at most 10, or dimension...

On Bailey pairs and certain q-series related to quadratic and ternary quadratic forms

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