Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Legendrian Varieties   Real Legendrian subvarieties are classical objects of differential geometry
and classical mechanics and they have been studied since antiquity. However,
complex Legendrian subvarieties are much more rigid and have more exceptional
properties. The most remarkable case is the Legendrian subvarieties of
projective space and prior to the author's research only few smooth examples of
these were known.
  The first series of results of this thesis is related to the automorphism
group of any Legendrian subvariety in any projective contact manifold. The
connected component of this group (under suitable minor assumptions) is
completely determined by the sections of the distinguished line bundle on the
contact manifold vanishing on the Legendrian variety. Moreover its action
preserves the contact structure.
  The second series of results is devoted to finding new examples of smooth
Legendrian subvarieties of projective space. The contribution of this thesis is
in three steps: First we find an example of a smooth toric surface. Next we
find a smooth quasihomogeneous Fano 8-fold that admits a Legendrian embedding.
Finally, we realise that both of these are special cases of a very general
construction: a general hyperplane section of a smooth Legendrian variety,
after a suitable projection, is a smooth Legendrian variety of smaller
dimension. By applying this result to known examples and decomposable
Legendrian varieties, we construct infinitely many new examples in every
dimension, with various Picard rank, canonical degree, Kodaira dimension and
other invariants.

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The categories of this paper are: cs
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph