10 papers
A toric Calabi-Yau counterexample to Schimpf's connected stable pairs pole conjecture
Reginald Anderson
Schimpf's connected reformulation of Pandharipande's pole conjecture for stable pairs predicts the following restriction: in class \(β\), connected descendent coefficients have non…
Planar rank-one sheaves on , obstruction bundles, and divisor-supported Donaldson--Thomas series
Reginald Anderson
Let and let \[ α_n=(0,1,-\tfrac12,\tfrac16-n)\in H^{\mathrm{even}}(X,\mathbb{Q}) \] with respect to the basis , where . We pr…
Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing
Reginald Anderson
We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce…
Rationality of cohomological descendent series for Quot schemes on surfaces with
Reginald Anderson
For a smooth projective surface , Johnson--Oprea--Pandharipande defined cohomological descendent generating series for Quot schemes of rank- quotients of $\OO_S^{\oplus N}$.…
The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
Reginald Anderson, Dominic Joyce
Let be a projective complex 3-manifold. An effective curve class is called positive if , and superpositive if all the effective summands…
Exceptional Collections for Toric Fano Fivefolds
Reginald Anderson
Resolutions of the diagonal of toric varieties has been an active area of study since Beilinson's celebrated resolution of the diagonal for $\PP^n$ and the disproof of King's conje…
Enumerative Geometry and Tree-Level Gromov--Witten Invariants
Reginald Anderson, Carrie Frizzell
Here we review background in differential topology related to the calculation of an euler characteristic, and background on localization in equivariant cohomology. We then outline…
Exceptional Collections for Toric Fano Fourfolds
Jumari Querimit Ramirez, Hill Zhang, Justin Son +1
Beilinson first gave a resolution of the diagonal for . Generalizing this, a modification of the cellular resolution of the diagonal given by Bayer-Popescu- Sturmfels…
Exceptional Collections of Line Bundles for Smooth Toric Fano Surfaces and Threefolds
Reginald Anderson
The cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels for unimodular projective toric varieties yields a full, strong exceptional collection of line bundles on u…
A Resolution of the Diagonal for Smooth Projective Toric Varieties
Reginald Anderson
The cellular construction of Bayer-Popescu-Sturmfels extends Beilinson's diagonal resolution from projective space to projective toric varieties whose lattice of principal divisors…