Kaloyan Slavov

activity

20122026

most citedAn application of random plane slicing to counting

F_{q}

-points on hypersurfaces

9 citations · 24 across the 13 of their papers we have counts for

collaborators

13 papers

math.AG2026

Sharp bounds for frame counts and setwise stabilizers in classical groups

Kaloyan Slavov

Let $k$ be a field, let $V = k^{n}$ , and let $G$ be a classical group acting on $V$ . For a finite subset $E \subset V$ and a basis $u = (u_{1}, \dots, u_{n})$ of $V$ , we study the set of $G$ -fr…

math.CO2025

Sets preserved by a large subgroup of the special linear group

Le Quang Hung, Thang Pham, Kaloyan Slavov

Let $E$ be a subset of the affine plane over a finite field $F_{q}$ . We bound the size of the subgroup of $S L_{2} (F_{q})$ that preserves $E$ . As a consequence, we show…

math.AG2024

Square values of several polynomials over a finite field

Kaloyan Slavov

Let $f_{1}, \dots, f_{m}$ be polynomials in $n$ variables with coefficients in a finite field $F_{q}$ . We estimate the number of points $x$ in $F_{q}^{n}$ such th…

math.GR2021

The proportion of derangements characterizes the symmetric and alternating groups

Bjorn Poonen, Kaloyan Slavov

Let $G$ be a subgroup of the symmetric group $S_{n}$ . If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_{n}$ ,…

math.AG2021

Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field

Kaloyan Slavov

We sharpen to nearly optimal the known asymptotic and explicit bounds for the number of $F_{q}$ -rational points on a geometrically irreducible hypersurface over a (large) fi…

math.AG2020★ 4 cited

The exceptional locus in the Bertini irreducibility theorem for a morphism

Bjorn Poonen, Kaloyan Slavov

We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we…

math.AG2019

Factorization type probabilities of polynomials with prescribed coefficients over a finite field

Kaloyan Slavov

Let $f (T)$ be a monic polynomial of degree $d$ with coefficients in a finite field $F_{q}$ . Extending earlier results in the literature, but now allowing $(q, 2 d) > 1$ , we give…

math.AG2017★ 9 cited

An application of random plane slicing to counting $F_{q}$ -points on hypersurfaces

Kaloyan Slavov

Let $X$ be an absolutely irreducible hypersurface of degree $d$ in $A^{n}$ , defined over a finite field $F_{q}$ . The Lang-Weil bound gives an interval that contains $…

math.AG2014★ 1 cited

Variants of the Kakeya problem over an algebraically closed field

Kaloyan Slavov

First, we study constructible subsets of $\A^n_k$ which contain a line in any direction. We classify the smallest such subsets in $\A^3$ of the type $R \cup {g \neq = 0},$ where $g\in…

math.AG2014★ 2 cited

An algebraic geometry version of the Kakeya problem

Kaloyan Slavov

We propose an algebraic geometry framework for the Kakeya problem. We conjecture that for any polynomials $f,g\in\F_{q_0}[x,y]$ and any $\F_q/\F_{q_0}$, the image of the map $\F_q^…

math.AG2012★ 1 cited

On the moduli space of hypersurfaces singular along a subscheme of large dimension but small degree

Kaloyan Slavov

Let $k$ be an algebraically closed field. Fix integers $n$ and $b$ with $n \geq 3$ and $1 \leq b \leq n - 1.$ Let $T_{k}^{d}$ be the moduli space of hypersurfaces $[F]$ in $P_{k}^{n}$ …

math.AG2012★ 5 cited

The moduli space of hypersurfaces whose singular locus has high dimension

Kaloyan Slavov

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n \geq 3$ and $1 \leq b \leq n - 1.$ Consider the moduli space $X$ of hypersurfaces in $P_{k}^{n}$ o…

math.AG2012★ 2 cited

The Hilbert polynomial of a symbolic square

Kaloyan Slavov

Let $k$ be an algebraically closed field, and let $C \subset P_{k}^{n}$ be a reduced closed subscheme with ideal sheaf $I$ . Let $I^{< 2 >}$ be the second symb…

Sharp bounds for frame counts and setwise stabilizers in classical groups

Sets preserved by a large subgroup of the special linear group

Square values of several polynomials over a finite field

The proportion of derangements characterizes the symmetric and alternating groups

Improved Lang--Weil bounds for a geometrically irreducible hypersurface over a finite field

The exceptional locus in the Bertini irreducibility theorem for a morphism

Factorization type probabilities of polynomials with prescribed coefficients over a finite field

An application of random plane slicing to counting Fq​-points on hypersurfaces

Variants of the Kakeya problem over an algebraically closed field

An algebraic geometry version of the Kakeya problem

On the moduli space of hypersurfaces singular along a subscheme of large dimension but small degree

The moduli space of hypersurfaces whose singular locus has high dimension

The Hilbert polynomial of a symbolic square

An application of random plane slicing to counting $F_{q}$ -points on hypersurfaces