487 research outputs found
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
On line covers of finite projective and polar spaces
An - of lines of a finite projective space (of a
finite polar space ) is a set of lines of (of
) such that every point of (of ) contains
lines of , for some . Embed in .
Let denote the set of points of lying on the
extended lines of .
An -cover of is an -dual -cover if
there are two possibilities for the number of lines of contained in an
-space of . Basing on this notion, we characterize
-covers of such that is a
two-character set of . In particular, we show that if
is invariant under a Singer cyclic group of then it is an
-dual -cover.
Assuming that the lines of are lines of a symplectic polar space
(of an orthogonal polar space of parabolic
type), similarly to the projective case we introduce the notion of an
-dual -cover of symplectic type (of parabolic type). We prove that an
-cover of (of ) has this dual
property if and only if is a tight set of an Hermitian variety
or of (of or of ). We also provide some interesting examples of -dual
-covers of symplectic type of .Comment: 20 page
Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties
The main purpose of this paper is to present a conceptual approach to
understanding the extension of the Prym map from the space of admissible double
covers of stable curves to different toroidal compactifications of the moduli
space of principally polarized abelian varieties. By separating the
combinatorial problems from the geometric aspects we can reduce this to the
computation of certain monodromy cones. In this way we not only shed new light
on the extension results of Alexeev, Birkenhake, Hulek, and Vologodsky for the
second Voronoi toroidal compactification, but we also apply this to other
toroidal compactifications, in particular the perfect cone compactification,
for which we obtain a combinatorial characterization of the indeterminacy
locus, as well as a geometric description up to codimension six, and an
explicit toroidal resolution of the Prym map up to codimension four.Comment: 53 pages, AMS LaTeX, Appendix by Mathieu Dutour Sikiric, minor
revisions, to appear in JEM
- …