45 citations · 110 across the 20 of their papers we have counts for
30 papers
The Chern character of a coherent sheaf on a smooth projective hypersurface
David Favero, Tyler L. Kelly
Given a coherent sheaf on a smooth projective hypersurface X, we prove an explicit formula for its Chern character as a Cech cocycle in terms of the free resolution of the associat…
Nonsimplicial toric Nullstellensatz and stacky GKZ theory
Christine Berkesch, Daniel Erman, David Favero
We introduce a variant of the Cox ring using -Cartier divisors and use this to remedy various deficiencies of nonsimplicial toric varieties. Our main applications are:…
Kuznetsov Categories for Gauged Linear Sigma Models
David Favero, Daniel Kaplan, Tyler L. Kelly
We define Kuznetsov and anti-Kuznetsov categories for gauged linear sigma models. We show that for complete intersections of ample divisors in smooth projective toric varieties, th…
King's Conjecture and the Cox category
Matthew R. Ballard, Christine Berkesch, Michael K. Brown +6
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective…
Topological Koszulity for Category Algebras
David Favero, Pouya Layeghi
We give a topological description of Ext groups between simple representations of categories via a nerve type construction. We use it to show that the Koszulity of indiscretely bas…
Line Bundle Resolutions via the Coherent-Constructible Correspondence
David Favero, Mykola Sapronov
We consider a finite collection of line bundles introduced by Bondal on a smooth, projective toric variety . For any coherent sheaf on , we construct minimal resoluti…
Rouquier dimension is Krull dimension for normal toric varieties
David Favero, Jesse Huang
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull dimension. Our proof uses the coherent-…
Homotopy Path Algebras
David Favero, Jesse Huang
We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between…
General GLSM Invariants and Their Cohomological Field Theories
David Favero, Bumsig Kim
We construct GLSM invariants for a general choice of stability in both the narrow and broad sector cases and prove they form a Cohomological Field Theory. This is obtained by formi…
A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles
David Favero, Daniel Kaplan, Tyler L. Kelly
We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category which does not…
Exceptional Collections for Mirrors of Invertible Polynomials
David Favero, Daniel Kaplan, Tyler L. Kelly
We prove the existence of a full exceptional collection for the derived category of equivariant matrix factorizations of an invertible polynomial with its maximal symmetry group. T…
Windows for cdgas
Nitin K. Chidambaram, David Favero
We study a Fourier-Mukai kernel associated to a GIT wall-crossing for arbitrarily singular (not necessarily reduced or irreducible) affine varieties over any field. This kernel is…
Kernels for Grassmann Flops
Matthew R. Ballard, Nitin K. Chidambaram, David Favero +2
We develop a generalization of the -construction of the first author, Diemer, and the third author for Grassmann flips. This generalization provides a canonical idempotent kerne…
Fundamental Factorization of a GLSM, Part I: Construction
Ionut Ciocan-Fontanine, David Favero, Jérémy Guéré +2
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type…
Kernels from Compactifications
Matthew R. Ballard, Colin Diemer, David Favero
To any affine scheme with a -action, we provide a Bousfield colocalization on the equivariant derived category of modules by constructing, via homotopical methods, an…
Fractional Calabi-Yau Categories from Landau-Ginzburg Models
David Favero, Tyler L. Kelly
We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an ad…
Derived Categories of BHK Mirrors
David Favero, Tyler L. Kelly
We prove a derived analogue to the results of Borisov, Clarke, Kelly, and Shoemaker on the birationality of Berglund-Hubsch-Krawitz mirrors. Heavily bootstrapping off work of Seide…
Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces
Charles F. Doran, David Favero, Tyler L. Kelly
Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypers…
Proof of a Conjecture of Batyrev and Nill
David Favero, Tyler L. Kelly
We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and N…
On the Derived Categories of Degree d Hypersurface Fibrations
Matthew Ballard, Dragos Deliu, David Favero +2
We provide descriptions of the derived categories of degree hypersurface fibrations which generalize a result of Kuznetsov for quadric fibrations and give a relative version of…
A category of kernels for equivariant factorizations, II: further implications
Matthew Ballard, David Favero, Ludmil Katzarkov
We leverage the results of the prequel in combination with a theorem of D. Orlov to yield some results in Hodge theory of derived categories of factorizations and derived categorie…
Homological Projective Duality via Variation of Geometric Invariant Theory Quotients
Matthew Ballard, Dragos Deliu, David Favero +2
We provide a geometric approach to constructing Lefschetz collections and Landau-Ginzburg Homological Projective Duals from a variation of Geometric Invariant Theory quotients. Thi…
The Mori Program and Non-Fano Toric Homological Mirror Symmetry
Matthew Ballard, Colin Diemer, David Favero +2
In the case of toric varieties, we continue the pursuit of Kontsevich's fundamental insight, Homological Mirror Symmetry, by unifying it with the Mori program. We give a refined co…
On the Griffiths Groups of Fano Manifolds of Calabi-Yau Hodge Type
David Favero, Atanas Iliev, Ludmil Katzarkov
A deep result of Voisin asserts that the Griffiths group of a general non-rigid Calabi-Yau (CY) 3-fold is infinitely generated. This theorem builds on an earlier method of hers whi…