Dennis Tseng

activity

20112022

most citedThe Splitting Subspace Conjecture

24 citations · 51 across the 15 of their papers we have counts for

collaborators

21 papers

math.AG2022

Lines highly tangent to a hypersurface

Anand Patel, Eric Riedl, Geoffrey Smith +1

We study spaces of lines that meet a smooth hypersurface X in P^n to high order. As an application, we give a polynomial upper bound on the number of planes contained in a smooth d…

math.AG2021

A Universal Formula For Counting Cubic Surfaces

Anand Deopurkar, Anand Patel, Dennis Tseng

Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit…

math.CO2021★ 3 cited

Tautological classes of matroids

Andrew Berget, Christopher Eur, Hunter Spink +1

We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for studying matroids. Using…

math.AG2020★ 4 cited

Moduli of linear slices of high degree hypersurfaces

Anand Patel, Eric Riedl, Dennis Tseng

We study the variation of linear sections of hypersurfaces in $P^{n}$ . We completely classify all plane curves, necessarily singular, whose line sections do not vary maximal…

math.AG2020★ 1 cited

Log-concavity of matroid h-vectors and mixed Eulerian numbers

Andrew Berget, Hunter Spink, Dennis Tseng

For any matroid $M$ , we compute the Tutte polynomial $T_{M} (x, y)$ using the mixed intersection numbers of certain classes in the combinatorial Chow ring $A^{∙} (M)$ arising from h…

math.AG2019

A note on $r$ hypersurfaces intersecting in $P^{r}$

Dennis Tseng

We consider the locus of $r$ -tuples of homogeneous forms of some fixed degree whose common vanishing locus in $P^{r}$ is positive dimensional. We show that any component of…

math.AG2019

On the EKL-Degree of a Weyl Cover

Joseph Knight, Ashvin Swaminathan, Dennis Tseng

More than four decades ago, Eisenbud, Khimšiašvili, and Levine introduced an analogue in the algebro-geometric setting of the notion of local degree from differential topology. The…

math.AG2019★ 7 cited

On the slope of the moduli space of genus 15 and 16 curves

Dennis Tseng

We revisit the work of Chang and Ran on bounding the slopes of $M_{15}$ and $M_{16}$ , correct one of the formulas used at the conclusion o…

math.AG2019★ 1 cited

Incidence strata of affine varieties with complex multiplicities

Hunter Spink, Dennis Tseng

To each affine variety $X$ and $m_{1}, \dots, m_{k} \in C$ such that no subset of the $m_{i}$ add to zero, we construct a variety which for $m_{1}, \dots, m_{k} \in N$ special…

math.AG2019

Equivariant Degenerations of Plane Curve Orbits

Mitchell Lee, Anand Patel, Dennis Tseng

In a series of papers, Aluffi and Faber computed the degree of the $G L_{3}$ orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by stu…

math.AG2019

Divisors on the moduli space of curves from divisorial conditions on hypersurfaces

Dennis Tseng

In this note, we extend work of Farkas and Rimányi on applying quadric rank loci to finding divisors of small slope on the moduli space of curves by instead considering all divisor…

math.AG2018★ 7 cited

An arithmetic count of the lines meeting four lines in P^3

Padmavathi Srinivasan, Kirsten Wickelgren

We enrich the classical count that there are two complex lines meeting four lines in space to an equality of isomorphism classes of bilinear forms. For any field $k$ , this enrichme…

math.AG2018★ 2 cited

$P G L_{2}$ -equivariant strata of point configurations in $P^{1}$

Hunter Spink, Dennis Tseng

We compute the integral Chow ring of the quotient stack $[(P^{1})^{n} / P G L_{2}]$ , which contains $M_{0, n}$ as a dense open, and determine a natural $Z$ -basis f…

math.AG2018★ 2 cited

Orbits in $(P^{r})^{n}$ and equivariant quantum cohomology

Mitchell Lee, Anand Patel, Hunter Spink +1

We compute the $G L_{r + 1}$ -equivariant Chow class of the $G L_{r + 1}$ -orbit closure of any point $(x_{1}, \dots, x_{n}) \in (P^{r})^{n}$ in terms of the rank polytope of the matroid…

math.AG2017

Complete families of immersed curves

Dennis Tseng

We extend results of Chang and Ran regarding large dimensional families of immersed curves of positive genus in projective space in two directions. In one direction, we prove a sha…

math.AG2017

A note on rational curves on general Fano hypersurfaces

Dennis Tseng

We show the Kontsevich space of rational curves of degree at most roughly $\frac{2 - 2}{2} n$ on a general hypersurface $X \subset P^{n}$ of degree $n - 1$ is equidimension…

math.AG2017

On degenerate sections of vector bundles

Dennis Tseng

We consider the locus of sections of a vector bundle on a projective scheme that vanish in higher dimension than expected. We show that after applying a high enough twist, any maxi…

math.AG2017

Collections of hypersurfaces containing a curve

Dennis Tseng

We consider the closed locus of $r$ -tuples of hypersurfaces in $P^{r}$ with positive dimensional intersection, and show in a large range of degrees that its largest componen…

math.CO2013

Critical groups of covering, voltage, and signed graphs

Victor Reiner, Dennis Tseng

Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular cover…

math.CO2012★ 24 cited

The Splitting Subspace Conjecture

Eric Chen, Dennis Tseng

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade a…

math.CO2011

Generalized Nonaveraging Integer Sequences

Dennis Tseng

Let the sequence S_m of nonnegative integers be generated by the following conditions: Set the first term a_0 = 0, and for all k \geq 0, let a_k+1 be the least integer greater than…

Lines highly tangent to a hypersurface

A Universal Formula For Counting Cubic Surfaces

Tautological classes of matroids

Moduli of linear slices of high degree hypersurfaces

Log-concavity of matroid h-vectors and mixed Eulerian numbers

A note on r hypersurfaces intersecting in Pr

On the EKL-Degree of a Weyl Cover

On the slope of the moduli space of genus 15 and 16 curves

Incidence strata of affine varieties with complex multiplicities

Equivariant Degenerations of Plane Curve Orbits

Divisors on the moduli space of curves from divisorial conditions on hypersurfaces

An arithmetic count of the lines meeting four lines in P^3

PGL2​-equivariant strata of point configurations in P1

Orbits in (Pr)n and equivariant quantum cohomology

Complete families of immersed curves

A note on rational curves on general Fano hypersurfaces

On degenerate sections of vector bundles

Collections of hypersurfaces containing a curve

Critical groups of covering, voltage, and signed graphs

The Splitting Subspace Conjecture

Generalized Nonaveraging Integer Sequences

A note on $r$ hypersurfaces intersecting in $P^{r}$

$P G L_{2}$ -equivariant strata of point configurations in $P^{1}$

Orbits in $(P^{r})^{n}$ and equivariant quantum cohomology