On the intersection of ovoids sharing a polarity (Q934663)
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scientific article; zbMATH DE number 5306129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the intersection of ovoids sharing a polarity |
scientific article; zbMATH DE number 5306129 |
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On the intersection of ovoids sharing a polarity (English)
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30 July 2008
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In this article, an ovoidal fibration is used to show that any two ovoids of \(\text{PG}(3,q)\), \(q\) even, sharing a polarity, must meet in an odd number of points. This result was previously known only when one of the ovoids was an elliptic quadric or a Tits ovoid. It is also shown that an ovoid and an elliptic quadric of \(\text{PG}(3,q)\), sharing all of their tangents, must meet in \(1\pmod 4\) points.
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ovoid
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elliptic quadric
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projective space
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intersection
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polarity
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ovoidal fibration
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