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9 papers · 1 filter
Mutual position of two smooth quadrics over finite fields
Shamil Asgarli, Chi Hoi Yip
Given two irreducible conics and over a finite field with odd, we show that there are points in such…
Higher-dimensional Losev-Manin spaces and their geometry
Patricio Gallardo, Javier González-Anaya, José Luis González +1
The classical Losev-Manin space is a toric compactification of the moduli space of points in the affine line modulo translation and scaling. Motivated by this, we study its hig…
Existence of pencils with nonblocking hypersurfaces
Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip
We prove that there is a pencil of hypersurfaces in of any given degree over a finite field such that every -member of the pencil is not…
Proportion of blocking curves in a pencil
Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip
Let be a pencil of plane curves defined over with no -points in its base locus. We investigate the number of curves in whos…
Most plane curves over finite fields are not blocking
Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip
A plane curve of degree is called \emph{blocking} if every -line in the plane meets at some -point. We prove that the pro…
Plane curves giving rise to blocking sets over finite fields
Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip
In recent years, many useful applications of the polynomial method have emerged in finite geometry. Indeed, algebraic curves, especially those defined by Rédei-type polynomials, ar…