41 citations · 108 across the 18 of their papers we have counts for
21 papers
Kleinian orbifolds, Cohomological Hall Algebras, and Yangians
Francesco Sala, Olivier Schiffmann, Parth Shimpi
We establish, for each orbifold crepantly resolving a Kleinian singularity, the existence of the cohomological Hall algebra (COHA) of coherent sheaves supported on the exceptional…
Nilpotent cohomological Hall algebras of surfaces
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala +2
This paper develops a framework for systematically studying cohomological "Hecke operators" associated with modifications of coherent sheaves on a smooth surface along a fixed…
Flops and Hilbert schemes of space curve singularities
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala +1
Using pagoda flop transitions between smooth projective threefolds, a relation is derived between the Euler numbers of moduli spaces of stable pairs which are scheme-theoretically…
Cohomological Hall algebras, their categorification, and their representations via torsion pairs
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala
In this paper we provide a systematic way of producing representations of cohomological, K-theoretical and categorified Hall algebras, and study the output of our construction in s…
On the Chow ring of the classifying stack of algebraic tori
Francesco Sala
We investigate the structure of the Chow ring of the classifying stacks of algebraic tori, as it has been defined by B. Totaro. Some previous work of N. Karpenko, A. Merkurjev…
Shuffle algebras for quivers as quantum groups
Andrei Neguţ, Francesco Sala, Olivier Schiffmann
We define a quantum loop group associated to an arbitrary quiver and maximal set of deformation parameters, with generators indexed by $I \times \mathbb{…
McKay correspondence, cohomological Hall algebras and categorification
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala
Let denote the canonical resolution of the two dimensional Kleinian singularity of type ADE. In the present paper, we establish isomorphisms between the cohomo…
Two-dimensional categorified Hall algebras
Mauro Porta, Francesco Sala
In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure…
Fock space representation of the circle quantum group
Francesco Sala, Olivier Schiffmann
In [arXiv:1711.07391] we have defined quantum groups and , which can be interpreted as con…
Quantization of continuum Kac-Moody algebras
Andrea Appel, Francesco Sala
Continuum Kac-Moody algebras have been recently introduced by the authors and O. Schiffmann. These are Lie algebras governed by a continuum root system, which can be realized as un…
Continuum Kac-Moody algebras
Andrea Appel, Francesco Sala, Olivier Schiffmann
We introduce a new class of infinite-dimensional Lie algebras, which we refer to as continuum Kac-Moody algebras. Their construction is closely related to that of usual Kac-Moody a…
Cohomological Hall algebra of Higgs sheaves on a curve
Francesco Sala, Olivier Schiffmann
We define the cohomological Hall algebra of the (-dimensional) Calabi-Yau category of Higgs sheaves on a smooth projective curve , as well as its nilpotent…
The circle quantum group and the infinite root stack of a curve (with an appendix by Tatsuki Kuwagaki)
Francesco Sala, Olivier Schiffmann
In the present paper, we give a definition of the quantum group of the circle , and its fundamental repr…
N=2 quiver gauge theories on A-type ALE spaces
Ugo Bruzzo, Francesco Sala, Richard J. Szabo
We survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in gauge theories on ALE spaces base…
AGT relations for abelian quiver gauge theories on ALE spaces
Mattia Pedrini, Francesco Sala, Richard J. Szabo
We construct level one dominant representations of the affine Kac-Moody algebra on the equivariant cohomology groups of moduli spaces of rank one framed…
Instantons and framed sheaves on Kähler Deligne-Mumford stacks
Philippe Eyssidieux, Francesco Sala
We provide stacky generalizations of classical gauge-theoretic results inspired by Donaldson, the Uhlenbeck-Yau theorem and variants due to Bando and his collaborators. Moreover, w…
Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
Ugo Bruzzo, Mattia Pedrini, Francesco Sala +1
We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gaug…
Framed sheaves on projective stacks
Ugo Bruzzo, Francesco Sala
Given a normal projective irreducible stack over an algebraically closed field of characteristic zero we consider framed sheaves on , i.e., pairs $(\mathca…
Symplectic structures on moduli spaces of framed sheaves on surfaces
Francesco Sala
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of fra…
Restriction theorems for -(semi)stable framed sheaves
Francesco Sala
We provide a generalization of Mehta-Ramanathan theorems to framed sheaves: we prove that the restriction of a -semistable framed sheaf on a nonsingular projective irreducible v…
Representations of the Heisenberg algebra and moduli spaces of framed sheaves
Francesco Sala, Pietro Tortella
We give a `geometrical' construction of an action of a Heisenberg algebra on the homology of the moduli spaces of torsion free sheaves on a complex smooth connected projective surf…