7 citations · 21 across the 10 of their papers we have counts for
12 papers
Nef Hattori classes and products of projective lines
Daniel Álvarez, Andrew Clarke, Eduardo González
Let \(X\) be a smooth connected complex projective variety with an effective algebraic \(\mathbb C^{\times}\)-action, a nonempty finite fixed locus whose weights are \(\pm1\). We s…
Morphisms of double Lie groupoids: a simplicial approach
Daniel Álvarez, Kalin Krishna, Stefano Ronchi
Motivated by recent developments in generalized Kähler geometry, we study morphisms of double Lie groupoids from a simplicial viewpoint. We show that the codiagonal functor $\Wbar$…
Shifted lagrangian structures in Poisson geometry
Daniel Álvarez, Henrique Bursztyn, Miquel Cueca
This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic grou…
Morita equivalences, moduli spaces and flag varieties
Daniel Álvarez
Double Bruhat cells in a connected complex semisimple Lie group emerged as a crucial concept in the work of S. Fomin and A. Zelevinsky on total positivity and cluster algebras.…
Symplectic double groupoids and the generalized Kähler potential
Daniel Álvarez, Marco Gualtieri, Yucong Jiang
A description of the fundamental degrees of freedom underlying generalized Kähler geometry, which separates its holomorphic moduli from its compatible Riemannian metric in a simila…
Homological vector fields over differentiable stacks
Daniel Álvarez, Miquel Cueca
In this work we solve the problem of providing a Morita invariant definition of Lie and Courant algebroids over Lie groupoids. By relying on supergeometry, we view these structures…
Transitive Courant algebroids and double symplectic groupoids
Daniel Álvarez
In this work we extend the Lu-Weinstein construction of double symplectic groupoids to any Lie bialgebroid such that its associated Courant algebroid is transitive and its Atiyah a…
Poisson groupoids and moduli spaces of flat bundles over surfaces
Daniel Álvarez
Let be a compact connected and oriented surface with nonempty boundary and let be a Lie group equipped with a bi-invariant pseudo-Riemannian metric. The moduli space of fla…
Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds
D. Álvarez
In this work we study the integrability of quotients of quasi-Poisson manifolds. Our approach allows us to put several classical results about the integrability of Poisson quotient…
Complete Lie algebroid actions and the integrability of Lie algebroids
D. Álvarez
We give a new proof of the equivalence between the existence of a complete action of a Lie algebroid on a surjective submersion and its integrability. The main tools in our approac…
Integrability of quotients in Poisson and Dirac geometry
Daniel Álvarez
We study the integrability of Poisson and Dirac structures that arise from quotient constructions. From our results we deduce several classical results as well as new applications.…
Leaves of stacky Lie algebroids
Daniel Álvarez
We show that the leaves of an LA-groupoid which pass through the unit manifold are, modulo a connectedness issue, Lie groupoids. We illustrate this phenomenon by considering the co…