Displaying similar documents to “ 𝔽 1 -schemes and toric varieties.”

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...

On varieties of orgraphs

Alfonz Haviar, Gabriela Monoszová (2001)

Discussiones Mathematicae Graph Theory

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In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.

Bihomogeneous forms in many variables

Damaris Schindler (2014)

Journal de Théorie des Nombres de Bordeaux

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We count integer points on varieties given by bihomogeneous equations using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in using the standard approach for homogeneous varieties. Also, we consider counting functions where not all the variables have to lie in intervals of the same size, which arises as a natural question in the setting of bihomogeneous varieties. ...