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

Showing math.AGShow all

10 papers · 1 filter

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.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.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.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…