Displaying similar documents to “An effective Bertini theorem and the number of rational points of a normal complete intersection over a finite field”

Pre-Tango structures and uniruled varieties

Yoshifumi Takeda (2007)

Colloquium Mathematicae

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The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field...

Embedding theorems for spaces of ℝ-places of rational function fields and their products

Katarzyna Kuhlmann, Franz-Viktor Kuhlmann (2012)

Fundamenta Mathematicae

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We study spaces M(R(y)) of ℝ-places of rational function fields R(y) in one variable. For extensions F|R of formally real fields, with R real closed and satisfying a natural condition, we find embeddings of M(R(y)) in M(F(y)) and prove uniqueness results. Further, we study embeddings of products of spaces of the form M(F(y)) in spaces of ℝ-places of rational function fields in several variables. Our results uncover rather unexpected obstacles to a positive solution of the open question...

Stably rational algebraic tori

Valentin E. Voskresenskii (1999)

Journal de théorie des nombres de Bordeaux

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The rationality of a stably rational torus with a cyclic splitting field is proved.