A characterization of quadrics by intersection numbers

2007 ◽  
Vol 47 (1-3) ◽  
pp. 165-175 ◽  
Author(s):  
Jeroen Schillewaert
Keyword(s):  
Intersection Numbers

CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES

2018 ◽  
Vol 107 (1) ◽  
pp. 1-8 ◽  
Author(s):  
ANGELA AGUGLIA
Keyword(s):  
Projective Spaces ◽  
Intersection Numbers

We characterize Hermitian cones among the surfaces of degree$q+1$of$\text{PG}(3,q^{2})$by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of$\text{PG}(4,q^{2})$among quasi-Hermitian ones.

scholarly journals A Characterization of the Hermitian Variety in Finite 3-Dimensional Projective Spaces

10.37236/3416 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Vito Napolitano
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Intersection Numbers ◽  
Combinatorial Characterization ◽  
Hermitian Variety ◽  
3 Dimensional ◽  
Dimensional Projective Space

A combinatorial characterization of a non-singular Hermitian variety of the finite 3-dimensional projective space via its intersection numbers with respect to lines and planes is given.   A corrigendum was added on March 29, 2019.

scholarly journals On Baer cones in $$\mathrm {PG}(3, q)$$

2021 ◽  
Vol 112 (3) ◽  
Author(s):  
Vito Napolitano
Keyword(s):  
Projective Space ◽  
Prime Power ◽  
Intersection Numbers ◽  
Link Type ◽  
Similar Characterization

AbstractRecently, in Innamorati and Zuanni (J. Geom 111:45, 2020. 10.1007/s00022-020-00557-0) the authors give a characterization of a Baer cone of $$\mathrm {PG}(3, q^2)$$ PG ( 3 , q 2 ) , q a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in $$q^2+1$$ q 2 + 1 , $$q^2+q+1$$ q 2 + q + 1 or $$q^3+q^2+1$$ q 3 + q 2 + 1 points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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