D. Joyce

collaborators

5 papers

math.AG2026

The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds

Reginald Anderson, Dominic Joyce

Let $X$ be a projective complex 3-manifold. An effective curve class $I^^{2} \in H_{2} (X, Z)$ is called positive if $c_{1} (X) \cdot I^^{2} > 0$ , and superpositive if all the effective summan…

math.DG2026

B-complex manifolds with generalized corners. I. Newlander-Nirenberg Theorems

HÃ¼lya ArgÃ¼z, Dominic Joyce

We generalize complex manifolds to manifolds with corners $X$ , and to manifolds with generalized corners (g-corners) in the sense of the second author arXiv:1501.00401, using compl…

math.DG2025

Stratified manifolds with corners

Dominic Joyce

We define categories of stratified manifolds (s-manifolds) and stratified manifolds with corners (s-manifolds with corners). An s-manifold $X$ of dimension $n$ is a Hausdorff,…

math.AT2025

Bordism categories and orientations of gauge theory moduli spaces

Dominic Joyce, Markus Upmeier

This is the second paper of a series that develops a bordism-theoretic point of view on orientations in enumerative geometry. The first paper is arXiv:2312.06818. This paper focuse…

math.AT2025

Bordism categories and orientations of moduli spaces

Dominic Joyce, Markus Upmeier

To define enumerative invariants in geometry, one often needs orientations on moduli spaces of geometric objects. This monograph develops a new bordism-theoretic point of view on o…