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. 
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References

SHOWING 1-10 OF 33 REFERENCES
Hermitian Varieties in a Finite Projective Space PG(N, q 2)
The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another
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.
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
Codes and caps from orthogonal Grassmannians
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
...
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