104 research outputs found
Quaternary matroids are vf-safe
Binary delta-matroids are closed under vertex flips, which consist of the
natural operations of twist and loop complementation. In this note we provide
an extension of this result from GF(2) to GF(4). As a consequence, quaternary
matroids are "safe" under vertex flips (vf-safe for short). As an application,
we find that the matroid of a bicycle space of a quaternary matroid is
independent of the chosen representation. This extends a result of Vertigan [J.
Comb. Theory B (1998)] concerning the bicycle dimension of quaternary matroids.Comment: 8 pages, no figures, the contents of this paper is now merged into v2
of [arXiv:1210.7718] (except for this comment, v2 is identical to v1
Abelian Fourfolds of Weil type and certain K3 Double Planes
Double planes branched in 6 lines give a famous example of K3 surfaces. Their
moduli are well understood and related to abelian fourfolds of Weil type. We
compare these two moduli interpretations and in particular divisors on the
moduli spaces. On the K3 side, this is achieved with the help of elliptic
fibrations. We also study the Kuga-Satake correspondence on these special
divisors.Comment: 48 pages, 4 figures; v3: final version with several additions
suggested by the refere
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