Shamil Asgarli

activity

20172026

most citedVan Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields

15 citations · 54 across the 30 of their papers we have counts for

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23 papers · 1 filter

math.AG2026

Covering plane curves over finite fields with lines

Shamil Asgarli, Sarthak Dassarma, Dragos Ghioca +2

We prove that, for every fixed $d \geq 2$ and $ε > 0$ , the $F_{q}$ -points of a geometrically irreducible reflexive plane curve of degree $d$ over $F_{q}$ can b…

math.AG2026

A geometric approach to the density of rank-metric codes

Shamil Asgarli, Lian Duan, Nathan Kaplan +1

We study the asymptotic density of $F_{q}$ -point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to ra…

math.AG2025

Blocking sets from a union of plane curves

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

Motivated by a question of Erdős on blocking sets in a projective plane that intersect every line only a few times, several authors have used unions of algebraic curves to construc…

math.AG2025

Hypersurfaces passing through the Galois orbit of a point

Shamil Asgarli, Jonathan Love, Chi Hoi Yip

Asgarli, Ghioca, and Reichstein proved that if $K$ is a field with $∣ K ∣ > 2$ , then for any positive integers $d$ and $n$ , and separable field extension $L / K$ with degree $m=\binom{n+…

math.AG2024

Linear system of geometrically irreducible plane cubics over finite fields

Shamil Asgarli, Dragos Ghioca

We examine the maximum dimension of a linear system of plane cubic curves whose $F_{q}$ -members are all geometrically irreducible. Computational evidence suggests that such…

math.AG2024

Mutual position of two smooth quadrics over finite fields

Shamil Asgarli, Chi Hoi Yip

Given two irreducible conics $C$ and $D$ over a finite field $F_{q}$ with $q$ odd, we show that there are $q^{2} /4 + O (q^{3/2})$ points $P$ in $P^{2} (F_{q})$ such…

math.AG2023

Linear system of hypersurfaces passing through a Galois orbit

Shamil Asgarli, Dragos Ghioca, Zinovy Reichstein

Let $d$ and $n$ be positive integers, and $E / F$ be a separable field extension of degree $m = (n n + d)$ . We show that if $∣ F ∣ > 2$ , then there exists a point $P\in \mathbb{P}^n…

math.AG2023

Plane-filling curves of small degree over finite fields

Shamil Asgarli, Dragos Ghioca

A plane curve $C$ in $P^{2}$ defined over $F_{q}$ is called plane-filling if $C$ contains every $F_{q}$ -point of $P^{2}$ . Homma and Kim, building on the…

math.AG2023

Tangent-filling plane curves over finite fields

Shamil Asgarli, Dragos Ghioca

We study plane curves over finite fields whose tangent lines at smooth $F_{q}$ -points together cover all the points of $P^{2} (F_{q})$ .

math.AG2023★ 5 cited

Existence of pencils with nonblocking hypersurfaces

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

We prove that there is a pencil of hypersurfaces in $P^{n}$ of any given degree over a finite field $F_{q}$ such that every $F_{q}$ -member of the pencil is not…

math.AG2023

Proportion of blocking curves in a pencil

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

Let $L$ be a pencil of plane curves defined over $F_{q}$ with no $F_{q}$ -points in its base locus. We investigate the number of curves in $L$ whos…

math.AG2022★ 2 cited

Most plane curves over finite fields are not blocking

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

A plane curve $C \subset P^{2}$ of degree $d$ is called \emph{blocking} if every $F_{q}$ -line in the plane meets $C$ at some $F_{q}$ -point. We prove that the pro…

math.AG2022★ 5 cited

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…

math.AG2022★ 1 cited

Frobenius nonclassical hypersurfaces

Shamil Asgarli, Lian Duan, Kuan-Wen Lai

A smooth hypersurface over a finite field $F_{q}$ is called Frobenius nonclassical if the image of every geometric point under the $q$ -th Frobenius endomorphism remains in t…

math.AG2022

Linear families of smooth hypersurfaces over finitely generated fields

Shamil Asgarli, Dragos Ghioca, Zinovy Reichstein

Let $K$ be a finitely generated field. We construct an $n$ -dimensional linear system $L$ of hypersurfaces of degree $d$ in $P^{n}$ defined over $K$ such that each…

math.AG2022

Smoothness in pencils of hypersurfaces over finite fields

Shamil Asgarli, Dragos Ghioca

We study pencils of hypersurfaces over finite fields $F_{q}$ such that each of the $q + 1$ members defined over $F_{q}$ is smooth.

math.AG2020

On the proportion of transverse-free plane curves

Shamil Asgarli, Brian Freidin

We study the asymptotic proportion of smooth plane curves over a finite field $F_{q}$ which are tangent to every line defined over $F_{q}$ . This partially answers a q…

math.AG2020

Transverse linear subspaces to hypersurfaces over finite fields

Shamil Asgarli, Lian Duan, Kuan-Wen Lai

Ballico proved that a smooth projective variety $X$ of degree $d$ over a finite field of $q$ elements admits a smooth hyperplane section if $q \geq d (d - 1)^{d i m X}$ . In this paper,…

math.AG2020

A Bertini type theorem for pencils over finite fields

Shamil Asgarli, Dragos Ghioca

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.

math.AG2019

Bijective Cremona transformations of the plane

Shamil Asgarli, Kuan-Wen Lai, Masahiro Nakahara +1

We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutat…

math.AG2019★ 8 cited

Transverse lines to surfaces over finite fields

Shamil Asgarli, Lian Duan, Kuan-Wen Lai

We prove that if $S$ is a smooth reflexive surface in $P^{3}$ defined over a finite field $F_{q}$ , then there exists an $F_{q}$ -line meeting $S$ transversely p…

math.AG2018★ 5 cited

Sharp Bertini theorem for plane curves over finite fields

Shamil Asgarli

We prove that if $C$ is a reflexive smooth plane curve of degree $d$ defined over a finite field $F_{q}$ with $d \leq q + 1$ , then there is an $F_{q}$ -line $L$ that inte…

math.AG2017★ 6 cited

The Picard group of the moduli of smooth complete intersections of two quadrics

Shamil Asgarli, Giovanni Inchiostro

We study the moduli space of smooth complete intersections of two quadrics in $P^{n}$ by relating it to the geometry of the singular members of the corresponding pencils. Gi…