258 research outputs found
Constructing projective varieties in weighted flag varieties
We compute the Hilbert series of general weighted flag varieties and discuss
a computer-aided method to determine their defining equations. We apply our
results to weighted flag varieties coming from the Lie groups of type G_2 and
GL(6), to construct some families of polarised projective varieties in
codimensions 8 and 6, respectively.Comment: 17 pages, 1 figur
Polarized rigid del Pezzo surfaces in low codimension
We provide explicit graded constructions of orbifold del Pezzo surfaces with
rigid orbifold points of type \left\{k_i\times\frac{1}{r_i}(1,a_i): 3\le r_i
\le 10,k_i \in \ZZ_{\ge 0}\right\}; as well-formed and quasismooth varieties
embedded in some weighted projective space. In particular, we present a
collection of 147 such surfaces such that their image under their
anti-canonical embeddings can be described by using one of the following sets
of equations: a single equation, two linearly independent equations, five
maximal Pfaffians of skew symmetric matrix, and nine
minors of size 3 square matrix. This is a complete classification of such
surfaces under certain carefully chosen bounds on the weights of ambient
weighted projective spaces and it is largely based on detailed
computer-assisted searches by using the computer algebra system \textsc{magma}.Comment: 22 pages, 5 tables, An improved version after a referee's comment
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