Intersections of the Hermitian Surface with Irreducible Quadrics in Even Characteristic

@article{Aguglia2016IntersectionsOT,
  title={Intersections of the Hermitian Surface with Irreducible Quadrics in Even Characteristic},
  author={Angela Aguglia and Luca Giuzzi},
  journal={Electron. J. Comb.},
  year={2016},
  volume={23},
  pages={4}
}
We determine the possible intersection sizes of a Hermitian surface $\mathcal H$ with an irreducible quadric of ${\mathrm PG}(3,q^2)$ sharing at least a tangent plane at a common non-singular point when $q$ is even. 
View PDF on arXiv
4 Citations
Highly Influential Citations
1
Background Citations
3

4 Citations

Unifying the known infinite families of relative hemisystems on the Hermitian surface
In this paper, we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space $\mathrm{H}(3, q^2 )$, unifying all known infinite families. We use these…
Intersection sets, three-character multisets and associated codes
TLDR
New minimal intersection sets are constructed in AG (r,q2) sporting three intersection numbers with hyperplanes and linear error correcting codes with few weights are obtained, whose weight enumerator is determined.
A note on relative hemisystems of Hermitian generalised quadrangles
TLDR
A set of sufficient criteria for the construction of relative hemisystems of the Hermitian space H(3,q2) is introduced, unifying all known infinite families.
$t$-Intersection sets in $AG(r,q^2)$ and two-character multisets in $PG(3,q^2)$
In this article we construct new minimal intersection sets in $AG(r,q^2)$ with respect to hyperplanes, of size $q^{2r-1}$ and multiplicity $t$, where $t\in \{ q^{2r-3}-q^{(3r-5)/2},…

References

SHOWING 1-10 OF 33 REFERENCES
Functional codes arising from quadric intersections with Hermitian varieties
Projective Geometries Over Finite Fields
1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9.…
Codes defined by forms of degree 2 on Hermitian surfaces and Sørensen's conjecture
Finite projective spaces of three dimensions
This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field. It is the second and core volume of a three-volume treatise on finite projective…
Structure of functional codes defined on non-degenerate Hermitian varieties
Minimum distance of Symplectic Grassmann codes
3264 and All That: A Second Course in Algebraic Geometry
Introduction 1. Introducing the Chow ring 2. First examples 3. Introduction to Grassmannians and lines in P3 4. Grassmannians in general 5. Chern classes 6. Lines on hypersurfaces 7. Singular…
Line polar Grassmann codes of orthogonal type
Geometric approach to higher weights
The notion of higher (or generalized) weights of codes is just as natural as that of the classical Hamming weight. The authors adopt the geometric point of view and always treat the q-ary case. Some…
INTERSECTION THEORY
I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincaré dual of a submanifold 4 3. Smooth cycles and their…
...
...