1,142 research outputs found
Curves with Canonical Models on Scrolls
Let be an integral and projective curve whose canonical model lies
on a rational normal scroll of dimension . We mainly study some
properties on , such as gonality and the kind of singularities, in the case
where and is non-Gorenstein, and in the case where , the scroll
is smooth, and is a local complete intersection inside . We also
prove that a rational monomial curve with just one singular point lies on a
surface scroll if and only if its gonality is at most , and that it lies on
a threefold scroll if and only if its gonality is at most
On the Singular Scheme of Split Foliations
We prove that the tangent sheaf of a codimension one locally free
distribution splits as a sum of line bundles if and only if its singular scheme
is arithmetically Cohen-Macaulay. In addition, we show that a foliation by
curves is given by an intersection of generically transversal holomorphic
distributions of codimension one if and only if its singular scheme is
arithmetically Buchsbaum. Finally, we establish that these foliations are
determined by their singular schemes, and deduce that the Hilbert scheme of
certain arithmetically Buchsbaum schemes of codimension is birational to a
Grassmannian.Comment: 21 page
Polynomial ring representations of endomorphisms of exterior powers
A polynomial ring with rational coefficients is an irreducible representation
of Lie algebras of endomorphisms of exterior powers of a infinite countable
dimensional -vector space. We give an explicit description of it,
using suitable vertex operators on exterior algebras, which mimick those
occurring in the bosonic vertex representation of the Lie algebra ,
due to Date--Jimbo--Kashiwara and Miwa (DJKM).Comment: few typos corrected, references updated, comments are very welcom
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