570 research outputs found
Partial ovoids and partial spreads in symplectic and orthogonal polar spaces
We present improved lower bounds on the sizes of small maximal partial ovoids and small maximal partial spreads in the classical symplectic and orthogonal polar spaces, and improved upper bounds on the sizes of large maximal partial ovoids and large maximal partial spreads in the classical symplectic and orthogonal polar spaces. An overview of the status regarding these results is given in tables. The similar results for the hermitian classical polar spaces are presented in [J. De Beule, A. Klein, K. Metsch, L. Storme, Partial ovoids and partial spreads in hermitian polar spaces, Des. Codes Cryptogr. (in press)]
Quotients of AdS_{p+1} x S^q: causally well-behaved spaces and black holes
Starting from the recent classification of quotients of Freund--Rubin
backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter
subgroups of isometries, we investigate the physical interpretation of the
associated quotients by discrete cyclic subgroups. We establish which quotients
have well-behaved causal structures, and of those containing closed timelike
curves, which have interpretations as black holes. We explain the relation to
previous investigations of quotients of asymptotically flat spacetimes and
plane waves, of black holes in AdS and of Godel-type universes.Comment: 48 pages; v2: minor typos correcte
Some surfaces with maximal Picard number
For a smooth complex projective variety, the rank of the N\'eron-Severi group
is bounded by the Hodge number h^{1,1}. Varieties with rk NS = h^{1,1} have
interesting properties, but are rather sparse, particularly in dimension 2. We
discuss in this note a number of examples, in particular those constructed from
curves with special Jacobians.Comment: Some comments and references adde
Sets of generators blocking all generators in finite classical polar spaces
We introduce generator blocking sets of finite classical polar spaces. These
sets are a generalisation of maximal partial spreads. We prove a
characterization of these minimal sets of the polar spaces Q(2n,q), Q-(2n+1,q)
and H(2n,q^2), in terms of cones with vertex a subspace contained in the polar
space and with base a generator blocking set in a polar space of rank 2.Comment: accepted for J. Comb. Theory
Prym varieties and their moduli
We discuss the geometry of the moduli space of Prym varieties. The article is
based on series of lectures given in Bedlewo and Luminy. The first section of
the paper contains a detailed historical account of the lives of Friedrich Prym
and Friedrich Schottky.Comment: 35 pages, minor corrections and additions. To appear in
"Contributions to algebraic geometry" edited by P. Pragacz and published by
the EM
Calabi–Yau threefolds and moduli of abelian surfaces I
We describe birational models and decide the rationality/unirationality of moduli spaces d (and levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of Abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi–Yau threefolds with Euler characteristic zero
Universal abelian covers of superisolated singularities
We give explicit examples of Gorenstein surface singularities with integral
homology sphere link, which are not complete intersections. Their existence was
shown by Luengo-Velasco, Melle-Hernandez and Nemethi, thereby providing
counterexamples to the Universal abelian covering conjecture of Neumann and
Wahl.Comment: Some examples and explanations added; updated version. 23 page
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