Jumping deformations of complete toric varieties.

Sato, Hiroshi

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This is the text of a talk given at the XVII Convegno dellUnione Matematica Italiana held at Milano, September 8-13, 2003. I would like to thank Angelo Lopez and Ciro Ciliberto for the kind invitation to the conference. I survey some numerical conjectures and theorems concerning relations between the index, the pseudo-index and the Picard number of a Fano variety. The results I refer to are contained in the paper [3], wrote in collaboration with Bonavero, Debarre and Druel. ...

On the Classification of Toric Fano Varieties.

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Some inequalities between the class and the degree of a smooth complex projective manifold are given. Application to the case of low sectional genus are supplied.

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Algebraic Legendrian varieties

Jarosław Buczyński

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Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity (see [Arn74], [Sła91] and references therein). However, complex Legendrian subvarieties are much more rigid and have more exceptional properties. The most remarkable case is the Legendrian subvarieties of projective space; prior to the author's research only few smooth examples of these were known (see [Bry82], [LM07]). Strong restrictions on...

On the Existence of Certain Smooth Toric Varieties.

B. Sturmfels, P. Kleinschmidt, J. Gretenkort (1990)

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