# A family of varieties with exactly one pointless rational fiber

Bianca Viray^{[1]}

- [1] Mathematics Department Box 1917 Brown University Providence, RI 02912 USA

Journal de Théorie des Nombres de Bordeaux (2010)

- Volume: 22, Issue: 3, page 741-745
- ISSN: 1246-7405

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topViray, Bianca. "A family of varieties with exactly one pointless rational fiber." Journal de Théorie des Nombres de Bordeaux 22.3 (2010): 741-745. <http://eudml.org/doc/116431>.

@article{Viray2010,

abstract = {We construct a concrete example of a $1$-parameter family of smooth projective geometrically integral varieties over an open subscheme of $\mathbb\{P\}^1_\{\mathbb\{Q\}\}$ such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.},

affiliation = {Mathematics Department Box 1917 Brown University Providence, RI 02912 USA},

author = {Viray, Bianca},

journal = {Journal de Théorie des Nombres de Bordeaux},

language = {eng},

number = {3},

pages = {741-745},

publisher = {Université Bordeaux 1},

title = {A family of varieties with exactly one pointless rational fiber},

url = {http://eudml.org/doc/116431},

volume = {22},

year = {2010},

}

TY - JOUR

AU - Viray, Bianca

TI - A family of varieties with exactly one pointless rational fiber

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2010

PB - Université Bordeaux 1

VL - 22

IS - 3

SP - 741

EP - 745

AB - We construct a concrete example of a $1$-parameter family of smooth projective geometrically integral varieties over an open subscheme of $\mathbb{P}^1_{\mathbb{Q}}$ such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.

LA - eng

UR - http://eudml.org/doc/116431

ER -

## References

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