430 research outputs found
Complete arcs arising from a generalization of the Hermitian curve
We investigate complete arcs of degree greater than two, in projective planes
over finite fields, arising from the set of rational points of a generalization
of the Hermitian curve. The degree of the arcs is closely related to the number
of rational points of a class of Artin-Schreier curves which is calculated by
using exponential sums via Coulter's approach. We also single out some examples
of maximal curves
Hyperbolic Structures and Root Systems
We discuss the construction of a one parameter family of complex hyperbolic
structures on the complement of a toric mirror arrangement associated with a
simply laced root system. Subsequently we find conditions for which parameter
values this leads to ball quotients
Gauge Theoretic Invariants of, Dehn Surgeries on Knots
New methods for computing a variety of gauge theoretic invariants for
homology 3-spheres are developed. These invariants include the Chern-Simons
invariants, the spectral flow of the odd signature operator, and the rho
invariants of irreducible SU(2) representations. These quantities are
calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k
Dehn surgery on (2,q) torus knots. The methods are then applied to compute the
SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M
Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff.
Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7
and 9.Comment: Version 3: minor corrections from version 2. Published by Geometry
and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.htm
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