Geoffrey Smith

activity

20142023

most citedCovering gonalities of complete intersections in positive characteristic

2 citations · 3 across the 12 of their papers we have counts for

collaborators

15 papers

math.AG2023

Stability of normal bundles of Brill-Noether curves

Izzet Coskun, Geoffrey Smith

We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $P^{r}$ is semistable if $g = 1$ or $g\geq \left \lceil \frac{5r}{2}\rig…

math.AG2022

Effective cycles on universal hypersurfaces

Geoffrey Smith

We study the effective cones of cycles on universal hypersurfaces on a projective variety $X$ , particularly focusing on the case of universal hypersurfaces in $P^{n}$ . We de…

math.AG2022

Stability and cohomology of kernel bundles on projective space

Izzet Coskun, Jack Huizenga, Geoffrey Smith

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_{1} \to V_{2}$ , where the $V_{i}$ are direct sums of line…

math.AG2021

Rational linear subspaces of hypersurfaces over finite fields

María Inés de Frutos Fernández, Sumita Garai, Kelly Isham +2

Let $X \subset P^{n}$ be a hypersurface of degree $d$ defined over a finite field of characteristic $p > 0$ . We prove that if $n \geq r + (r + 1 d + r)$ , then $X$ contains…

math.AG2021

Exceptional loci in Lefschetz theory

Sam Raskin, Geoffrey Smith

Let $ϕ : X \to P^{n}$ be a morphism of varieties. Given a hyperplane $H$ in $P^{n}$ , there is a Gysin map from the compactly supported cohomology of $ϕ^{- 1} (H)$ …

math.AG2021

Very free rational curves in Fano varieties

Izzet Coskun, Geoffrey Smith

Let $X$ be a projective variety and let $C$ be a rational normal curve on $X$ . We compute the normal bundle of $C$ in a general complete intersection of hypersurfaces of sufficient…