1,147 research outputs found
Coverings of graded pointed Hopf algebras
We introduce the concept of a covering of a graded pointed Hopf algebra. The
theory developed shows that coverings of a bosonized Nichols algebra can be
concretely expressed by biproducts using a quotient of the universal coalgebra
covering group of the Nichols algebra. If there are enough quadratic relations,
the universal coalgebra covering is given by the bosonization by the enveloping
group of the underlying rack.Comment: to appear in J. of Algebr
Hurwitz spaces of quadruple coverings of elliptic curves and the moduli space of abelian threefolds A_3(1,1,4)
We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds
with polarization of type (1,1,4) is unirational. By a result of Birkenhake and
Lange this implies the unirationality of the isomorphic moduli space
A_3(1,4,4). The result is based on the study the Hurwitz space H_{4,n}(Y) of
quadruple coverings of an elliptic curve Y simply branched in n points. We
prove the unirationality of its codimension one subvariety H^{0}_{4,A}(Y) which
parametrizes quadruple coverings \pi:X --> Y with Tschirnhausen modules
isomorphic to A^{-1}, where A\in Pic^{n/2}Y, and for which \pi^*:J(Y)--> J(X)
is injective. This is an analog of the result of Arbarello and Cornalba that
the Hurwitz space H_{4,n}(P^1) is unirational.Comment: 28 pages, amslatex, to appear in Mathematische Nachrichte
Covering functors without groups
Coverings in the representation theory of algebras were introduced for the
Auslander-Reiten quiver of a representation finite algebra by Riedtmann and
later for finite dimensional algebras by Bongartz and Gabriel, R.
Martinez-Villa and de la Pe\~na. The best understood class covering functors is
that of Galois covering functors F: A -> B determined by the action of a group
of automorphisms of A. In this work we introduce the balanced covering functors
which include the Galois class and for which classical Galois covering-type
results still hold. For instance, if F:A -> B is a balanced covering functor,
where A and B are linear categories over an algebraically closed field, and B
is tame, then A is tame.Comment: Some improvements have been made; in particular, the proof of Theorem
2 has been restructured and clarifie
Algebraic functions with even monodromy
Let be a compact Riemann surface of genus and be an
integer. We show that admits meromorphic functions with monodromy group
equal to the alternating group $A_d.
Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
We prove that the moduli spaces A_3(D) of polarized abelian threefolds with
polarizations of types D=(1,1,2), (1,2,2), (1,1,3) or (1,3,3) are unirational.
The result is based on the study of families of simple coverings of elliptic
curves of degree 2 or 3 and on the study of the corresponding period mappings
associated with holomorphic differentials with trace 0. In particular we prove
the unirationality of the Hurwitz space H_{3,A}(Y) which parameterizes simply
branched triple coverings of an elliptic curve Y with determinants of the
Tschirnhausen modules isomorphic to A^{-1}.Comment: 43 pages, latex2e, some typos corrected, references updated, to
appear in Annali di Matematica Pura ed Applicat
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