102 research outputs found
Infinitesimal deformations of restricted simple Lie algebras I
We compute the infinitesimal deformations of two families of restricted
simple modular Lie algebras of Cartan type: the Witt-Jacobson and the Special
Lie algebras.Comment: 27 pages, title slightly changed, references updated, typos
corrected, final version to appear on J. Algebr
Restricted simple Lie algebras and their infinitesimal deformations
In this expository paper, we first review the classification of the
restricted simple Lie algebras in characteristic different from 2 and 3 and
then we describe their infinitesimal deformations. We conclude by indicating
some possible application to the deformations of simple finite group schemes.Comment: 11 pages, An Introduction to the classification of restricted simple
Lie algebras and their deformation
Moduli and Periods of Supersymmetric Curves
Supersymmetric curves are the analogue of Riemann surfaces in super geometry.
We establish some foundational results about complex Deligne-Mumford
superstacks, and we then prove that the moduli superstack of supersymmetric
curves is a smooth complex Deligne-Mumford superstack. We then show that the
superstack of supersymmetric curves admits a coarse complex superspace, which,
in this case, is just an ordinary complex space. In the second part of this
paper we discuss the period map. We remark that the period domain is the moduli
space of ordinary abelian varieties endowed with a symmetric theta divisor, and
we then show that the differential of the period map is surjective. In other
words, we prove that any first order deformation of a classical Jacobian is the
Jacobian of a supersymmetric curve.Comment: Minor revision, to appear on Advances in Theoretical and Mathematical
Physic
Families of n-gonal curves with maximal variation of moduli
We study families of n-gonal curves with maximal variation of moduli, which
have a rational section. Certain numerical results on the degree of the modular
map are obtained for such families of hyperelliptic and trigonal curves. In the
last case we use the description of the relative Picard group of the universal
family of trigonal curves.Comment: 16 pages. Some modifications on the third section. References adde
Picard group of moduli of hyperelliptic curves
The main subject of this work is the difference between the coarse moduli
space and the stack of hyperelliptic curves. We compute their Picard groups,
giving explicit description of the generators. We get an application to the
(non-)existence of a tautological family over the coarse moduli space.Comment: 13 pages. Section 2 has been shortened and the final appendix has
been erased. Final version, to appear on Math. Zei
Comparing Perfect and 2nd Voronoi decompositions: the matroidal locus
We compare two rational polyhedral admissible decompositions of the cone of
positive definite quadratic forms: the perfect cone decomposition and the 2nd
Voronoi decomposition. We determine which cones belong to both the
decompositions, thus providing a positive answer to a conjecture of V. Alexeev
and A. Brunyate. As an application, we compare the two associated toroidal
compactifications of the moduli space of principal polarized abelian varieties:
the perfect cone compactification and the 2nd Voronoi compactification.Comment: 27 pages, 2 figures, final version, to appear in Mathematische
Annale
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