## Innovations in Incidence Geometry

- Innov. Incidence Geom.
- Volume 1, Number 1 (2005), 19-34.

### New results on covers and partial spreads of polar spaces

Andreas Klein and Klaus Metsch

#### Abstract

We investigate blocking sets of projective spaces that are contained in cones over quadrics of rank two. As an application we obtain new results on partial ovoids, partial spreads, and blocking sets of polar spaces. One of the results is that a partial ovoid of $H\left(3,{q}^{2}\right)$ with more than ${q}^{3}-q+1$ points is contained in an ovoid. We also give a new proof of the result that a partial spread of $Q\left(4,q\right)$ with more than ${q}^{2}-q+1$ lines is contained in a spread; this is the first common proof for even and odd $q$. Finally, we improve the lower bound on the size of a smallest blocking set of the symplectic polar space $W\left(3,q\right)$, $q$ odd.

#### Article information

**Source**

Innov. Incidence Geom., Volume 1, Number 1 (2005), 19-34.

**Dates**

Received: 30 July 2004

Accepted: 20 January 2005

First available in Project Euclid: 26 February 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.iig/1551206814

**Digital Object Identifier**

doi:10.2140/iig.2005.1.19

**Mathematical Reviews number (MathSciNet)**

MR2213952

**Zentralblatt MATH identifier**

1116.51010

**Subjects**

Primary: 05B25: Finite geometries [See also 51D20, 51Exx] 51E12: Generalized quadrangles, generalized polygons 51E20: Combinatorial structures in finite projective spaces [See also 05Bxx] 51E21: Blocking sets, ovals, k-arcs

**Keywords**

polar spaces, partial spreads partial ovoids blocking sets covers

#### Citation

Klein, Andreas; Metsch, Klaus. New results on covers and partial spreads of polar spaces. Innov. Incidence Geom. 1 (2005), no. 1, 19--34. doi:10.2140/iig.2005.1.19. https://projecteuclid.org/euclid.iig/1551206814