Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi–Yau 4-folds

Autor: Yalong Cao, Dominic Joyce, Jacob Gross

Suppose $(X,\Omega,g)$ is a compact Spin(7)-manifold, e.g. a Riemannian 8-manifold with holonomy Spin(7), or a Calabi-Yau 4-fold. Let $G$ be U$(m)$ or SU$(m)$, and $P\to X$ be a principal $G$-bundle. We show that the infinite-dimensional moduli space

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https://ora.ox.ac.uk/objects/uuid:39b727fa-ed9e-4445-9bae-84ebed035a21

The derived moduli stack of shifted symplectic structures

Autor: Valerio Melani, Samuel Bach

We introduce and study the derived moduli stack $\mathrm{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on $X$, we prove that $

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http://arxiv.org/abs/1706.08369

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

Autor: Ben-Bassat, Oren, Brav, Chris, Bussi, V, Joyce, Dominic, Bussi, Vittoria

Publikováno v: Geom. Topol. 19, no. 3 (2015), 1287-1359

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 and Vezzosi, arXiv:1111.3209. This paper extends the previous three fr

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http://ora.ox.ac.uk/objects/uuid:4c39c93c-ae37-4006-aac5-f71782a8e2ac

Poisson bivectors and Poisson brackets on affine derived stacks

Autor: Valerio Melani

Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on Spec(A) to the

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http://hdl.handle.net/11568/959760

Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes

Autor: Gabriele Vezzosi, Timo Schürg, Bertrand Toën

Publikováno v: Journal für die reine und angewandte Mathematik
Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2015, 702, pp.1-40. ⟨10.1515/crelle-2013-0037⟩
Journal für die reine und angewandte Mathematik, 2015, 702, pp.1-40. ⟨10.1515/crelle-2013-0037⟩
Journal für die Reine und Angewandte Mathematik

We show how a quasi-smooth derived enhancement of a Deligne-Mumford stack X naturally endows X with a functorial perfect obstruction theory in the sense of Behrend-Fantechi. This result is then applied to moduli of maps and perfect complexes on a smo

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