D. Joyce

activity

20092026

most citedA 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications

104 citations · 343 across the 17 of their papers we have counts for

collaborators

22 papers

math.DG2026

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

Hülya Argüz, 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.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 $β \in H_{2} (X, Z)$ is called positive if $c_{1} (X) \cdot β > 0$ , and superpositive if all the effective summands…

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 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…

math.AT2023

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.AG2021★ 5 cited

Enumerative invariants and wall-crossing formulae in abelian categories

Dominic Joyce

Enumerative invariants in Algebraic Geometry 'count' $τ$ -(semi)stable objects $E$ with fixed topological invariants $[E] = a$ in some geometric problem, using a virtual class $[{\cal…

math.AG2020

Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds

Dominic Joyce, Markus Upmeier

Let $X$ be a compact Calabi-Yau 3-fold, and write $M, M ˉ$ for the moduli stacks of objects in coh $(X), D^{b}$ coh $(X)$ . There are natural line bundles $K_{\mathca…

math.DG2019

On spin structures and orientations for gauge-theoretic moduli spaces

Dominic Joyce, Markus Upmeier

Let $X$ be a compact manifold, $G$ a Lie group, $P \to X$ a principal $G$ -bundle, and $B_{P}$ the infinite-dimensional moduli space of connections on $P$ modulo gauge. For…

math.DG2018★ 9 cited

Canonical orientations for moduli spaces of $G_{2}$ -instantons with gauge group SU(m) or U(m)

Dominic Joyce, Markus Upmeier

Suppose $(X, g)$ is a compact, spin Riemannian 7-manifold, with Dirac operator $D$ . Let $G$ be SU $(m)$ or U $(m)$ , and $E \to X$ be a rank $m$ complex bundle with $G$ -structure. Writ…

math.DG2018★ 24 cited

On orientations for gauge-theoretic moduli spaces

Dominic Joyce, Yuuji Tanaka, Markus Upmeier

Let $X$ be a compact manifold, $D$ a real elliptic operator on $X$ , $G$ a Lie group, $P \to X$ a principal $G$ -bundle, and $B_{P}$ the infinite-dimensional moduli space of…

math.DG2016★ 8 cited

Conjectures on counting associative 3-folds in $G_{2}$ -manifolds

Dominic Joyce

There is a strong analogy between compact, torsion-free $G_{2}$ -manifolds $(X, φ, * φ)$ and Calabi-Yau 3-folds $(Y, J, g, ω)$ . We can also generalize $(X, φ, * φ)$ to 'tamed almost $G_{2}$ -mani…

math.AT2015★ 4 cited

Some new homology and cohomology theories of manifolds and orbifolds

Dominic Joyce

For each manifold or effective orbifold $Y$ and commutative ring $R$ , we define a new homology theory $M H_{*} (Y; R)$ , $M$ - $h o m o l o g y$ , and a new cohomology theory $M H^{*} (Y; R)$ , $M$ -$coh…

math.AG2015★ 7 cited

A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes

Dominic Joyce, Pavel Safronov

Pantev, Toen, Vaquié and Vezzosi arXiv:1111.3209 defined $k$ -shifted symplectic derived schemes and stacks $X$ for $k \in Z$ , and Lagrangians ${\bf f}:{\bf L}\to{\bf X}…

math.AG2015★ 54 cited

Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds

Dennis Borisov, Dominic Joyce

Let $(X, ω_{X}^{*})$ be a separated, $- 2$ -shifted symplectic derived $C$ -scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual…

math.SG2014★ 18 cited

Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m

Yohsuke Imagi, Dominic Joyce, Joana Oliveira dos Santos

We prove two main results: (a) Suppose $L$ is a closed, embedded, exact special Lagrangian $m$ -fold in $C^{m}$ for $m \geq 3$ asymptotic at infinity to the union $Π_{1} \cup Π_{2}$ …

math.DG2014★ 36 cited

Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow

Dominic Joyce

Let $M$ be a Calabi-Yau $m$ -fold, and consider compact, graded Lagrangians $L$ in $M$ . Thomas and Yau math.DG/0104196, math.DG/0104197 conjectured that there should be a notion of…

math.AG2013★ 104 cited

A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications

Oren Ben-Bassat, Christopher Brav, Vittoria Bussi +1

This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the ' $k$ -shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie…

math.AG2013

On motivic vanishing cycles of critical loci

Vittoria Bussi, Dominic Joyce, Sven Meinhardt

Let $U$ be a smooth scheme over an algebraically closed field $K$ of characteristic zero and $f : U \to A^{1}$ a regular function, and write $X =$ Crit $(f)$ , as a closed…

math.AG2013

A 'Darboux theorem' for derived schemes with shifted symplectic structure

Christopher Brav, Vittoria Bussi, Dominic Joyce

We prove a 'Darboux theorem' for derived schemes with symplectic forms of degree $k < 0$ , in the sense of Pantev, Toen, Vaquie and Vezzosi arXiv:1111.3209. More precisely, we show th…

math.AG2013

A classical model for derived critical loci

Dominic Joyce

Let $f : U \to A^{1}$ be a regular function on a smooth scheme $U$ over a field $K$ . Pantev, Toen, Vaquie and Vezzosi (arXiv:1111.3209, arXiv:1109.5213) define the "der…

math.AG2012★ 73 cited

Symmetries and stabilization for sheaves of vanishing cycles

Christopher Brav, Vittoria Bussi, Delphine Dupont +2

Let $U$ be a smooth $C$ -scheme, $f : U \to A^{1}$ a regular function, and $X =$ Crit $(f)$ the critical locus, as a $C$ -subscheme of $U$ . Then one can define the "pe…

math.DG2009★ 1 cited

On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

Dominic Joyce, Yng-Ing Lee, Richard Schoen

Let (M,w) be a compact symplectic 2n-manifold, and g a Riemannian metric on M compatible with w. For instance, g could be Kahler, with Kahler form w. Consider compact Lagrangian su…

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

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

Stratified manifolds with corners

Bordism categories and orientations of moduli spaces

Bordism categories and orientations of gauge theory moduli spaces

Enumerative invariants and wall-crossing formulae in abelian categories

Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds

On spin structures and orientations for gauge-theoretic moduli spaces

Canonical orientations for moduli spaces of G2​-instantons with gauge group SU(m) or U(m)

On orientations for gauge-theoretic moduli spaces

Conjectures on counting associative 3-folds in G2​-manifolds

Some new homology and cohomology theories of manifolds and orbifolds

A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes

Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds

Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in C^m

Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow

A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications

On motivic vanishing cycles of critical loci

A 'Darboux theorem' for derived schemes with shifted symplectic structure

A classical model for derived critical loci

Symmetries and stabilization for sheaves of vanishing cycles

On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds

Canonical orientations for moduli spaces of $G_{2}$ -instantons with gauge group SU(m) or U(m)

Conjectures on counting associative 3-folds in $G_{2}$ -manifolds