Contact Moishezon threefolds with second Betti number one
We prove that the only contact Moishezon threefold having second Betti number equal to one is the projective space.
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arXiv subjects
Jaroslaw Buczynski
Publications and source records attributed to Jaroslaw Buczynski.
Toric Legendrian subvarieties
We give the full classification of smooth toric Legendrian subvarieties in projective space. We also prove that under some minor assumptions the group of linear automorphisms preserving given Legendrian subvariety preserves the contact structure of the ambient projective space.
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Hyperplane sections of Legendrian subvarieties
We prove that a general hyperplane section of a smooth Legendrian subvariety in a projective space admits Legendrian embedding into another projective space. This gives numerous new examples of smooth Legendrian subvarieties, some of which have positive Kodaira dimension.
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Some quasihomogeneous Legendrian varieties
We construct a family of examples of Legendrian subvarieties in some projective spaces. Although most of them are singular, a new example of smooth Legendrian variety in dimension 8 is in this family. The 8-fold has interesting properties: it is a compactification of the special linear group, a Fano manifold of index 5 and Picard number 1.
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Properties of legendrian subvarieties of projective space
I prove that every smooth legendrian variety generated by quadrics is a homogeneous variety and further I give a list of all such legendrian varieties. A review of the subject is included, illustrated by examples. Another result is that no complete intersection is a legendrian variety.
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