64 citations · 192 across the 16 of their papers we have counts for
18 papers
Equivariant toric geometry and Euler-Maclaurin formulae -- an overview
Sylvain E. Cappell, Laurenţiu Maxim, Jörg Schürmann +1
We survey recent developments in the study of torus equivariant motivic Chern and Hirzebruch characteristic classes of projective toric varieties, with applications to calculating…
Equivariant toric geometry and Euler-Maclaurin formulae
Sylvain E. Cappell, Laurenţiu Maxim, Jörg Schürmann +1
We consider equivariant versions of the motivic Chern and Hirzebruch characteristic classes of a quasi-projective toric variety, and extend many known results from non-equivariant…
D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces
Antonella Grassi, James Halverson, Cody Long +3
In this paper we study the 6d localized charged matter spectrum of F-theory directly on a singular elliptic Calabi-Yau 3-fold, i.e. without smoothing via resolution or deformation…
Signatures of topological branched covers
Christian Geske, Alexandra Kjuchukova, Julius L. Shaneson
Let and be smooth manifolds and a branched cover with branching set . Classically, if is smoothly embedded in , the signature can be comput…
Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces
Antonella Grassi, James Halverson, Cody Long +2
We demonstrate how non-simply-laced gauge and flavor symmetries arise in F-theory on spaces with non-isolated singularities. The breaking from a simply-laced symmetry to one that i…
Dualities of Deformed SCFTs from Link Monodromy on D3-brane States
Antonella Grassi, James Halverson, Fabian Ruehle +1
We study D3-brane theories that are dually described as deformations of two different superconformal theories with massless monopoles and dyons. These arise at the…
Geometry and Topology of String Junctions
Antonella Grassi, James Halverson, Julius L. Shaneson
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their propertie…
Non-Higgsable QCD and the Standard Model Spectrum in F-theory
Antonella Grassi, James Halverson, Julius Shaneson +1
Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clu…
Estimates on Lattice Points in the Circle
Julius L. Shaneson
This paper provides estimates on the difference between the number of integer lattice points an a circle centered at the origin and the area. The estimates have the form "Big O" of…
Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-theory
Antonella Grassi, James Halverson, Julius L. Shaneson
Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Ac…
Matter From Geometry Without Resolution
Antonella Grassi, James Halverson, Julius L. Shaneson
We utilize the deformation theory of algebraic singularities to study charged matter in compactifications of M-theory, F-theory, and type IIa string theory on elliptically fibered…
Characteristic classes of symmetric products of complex quasi-projective varieties
Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann +2
We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homo…
Equivariant characteristic classes of singular complex algebraic varieties
Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann +1
Homology Hirzebruch characteristic classes for singular varieties have been recently defined by Brasselet-Schuermann-Yokura as an attempt to unify previously known characteristic c…
Characteristic classes of complex hypersurfaces
Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann +1
The Milnor-Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincare dual of the) Hirzebruch class of the virtu…
Hodge genera of algebraic varieties, II
Sylvain E. Cappell, Anatoly Libgober, Laurentiu Maxim +1
We study the behavior of Hodge-theoretic genera under morphisms of complex algebraic varieties. We prove that the additive -genus which arises in the motivic context satisfies…
Some Problems in Number Theory I: The Circle Problem
Sylvain E. Cappell, Julius L. Shaneson
This paper concerns the number of lattice points in a circle.
Euler characteristics of algebraic varieties
Sylvain E. Cappell, Laurentiu Maxim, Julius L. Shaneson
This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods a…
Genera of algebraic varieties and counting of lattice points
Sylvain E. Cappell, Julius L. Shaneson
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology anal…