41 citations · 194 across the 19 of their papers we have counts for
26 papers
Clusters, twistors and stability conditions I
Tom Bridgeland, Helge Ruddat
We consider a quiver of ADE type and use cluster combinatorics to define two complex manifolds and . The space can be identified with a qu…
Intrinsic enumerative mirror symmetry: Takahashi's log mirror symmetry for revisited
Michel van Garrel, Helge Ruddat, Bernd Siebert
Let be a smooth cubic in the projective plane . Nobuyoshi Takahashi formulated a conjecture that expresses counts of rational curves of varying degree in $\mathbb…
Singular Log Structures and Log Crepant Log Resolutions I
Alessio Corti, Tim Graefnitz, Helge Ruddat
We introduce a class of singular log schemes in three dimensions and conjecture that log schemes in this class admit log crepant log resolutions. We provide examples as evidence an…
Enumerative Geometry of Quantum Periods
Tim Gräfnitz, Helge Ruddat, Eric Zaslow +1
We interpret the -refined theta function of a log Calabi-Yau surface as a natural -refinement of the open mirror map, defined by quantum period…
How to make log structures
Alessio Corti, Helge Ruddat
We introduce the concept of a viable generically Gorenstein toroidal crossing (ggtc) space . This generalizes the concept of Gorenstein toroidal crossing scheme, which in turn g…
The proper Landau-Ginzburg potential is the open mirror map
Tim Gräfnitz, Helge Ruddat, Eric Zaslow
The mirror dual of a smooth toric Fano surface equipped with an anticanonical divisor is a Landau-Ginzburg model with superpotential, W. Carl-Pumperla-Siebert give a defini…
Compactifying torus fibrations over integral affine manifolds with singularities
Helge Ruddat, Ilia Zharkov
This is an announcement of the following construction: given an integral affine manifold with singularities, we build a topological space which is a torus fibration over $B…
A homology theory for tropical cycles on integral affine manifolds and a perfect pairing
Helge Ruddat
We introduce a cap product pairing for homology and cohomology of tropical cycles on integral affine manifolds with singularities. We show the pairing is perfect over …
Tailoring a pair of pants
Helge Ruddat, Ilia Zharkov
We show how to deform the map such that the image of the complex pair of pants is…
Smoothing toroidal crossing spaces
Simon Felten, Matej Filip, Helge Ruddat
We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very co…
Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations
Helge Ruddat, Bernd Siebert
We give a simple expression for the integral of the canonical holomorphic volume form in degenerating families of varieties constructed from wall structures and with central fiber…
Tropically constructed Lagrangians in mirror quintic threefolds
Cheuk Yu Mak, Helge Ruddat
We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. We apply this construc…
Tropical quantum field theory, mirror polyvector fields, and multiplicities of tropical curves
Travis Mandel, Helge Ruddat
We introduce algebraic structures on the polyvector fields of an algebraic torus that serve to compute multiplicities in tropical and log Gromov-Witten theory while also connecting…
Local uniqueness of approximations and finite determinacy of log morphisms
Helge Ruddat
I prove a local finite determinacy result of singular fibres in families. As an application, I generalize finite determinacy results on the fibres of log morphisms and nearby and v…
The degeneration formula for stable log maps
Bumsig Kim, Hyenho Lho, Helge Ruddat
We give a short direct proof for the degeneration formula of Gromov-Witten invariants including its cycle version for degenerations with smooth singular locus in the setting of min…
Local Gromov-Witten Invariants are Log Invariants
Michel van Garrel, Tom Graber, Helge Ruddat
We prove a simple equivalence between the virtual count of rational curves in the total space of an anti-nef line bundle and the virtual count of rational curves maximally tangent…
Descendant log Gromov-Witten invariants for toric varieties and tropical curves
Travis Mandel, Helge Ruddat
Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric variet…
Motivic Zeta Functions of the Quartic and its Mirror Dual
Johannes Nicaise, D. Peter Overholser, Helge Ruddat
We use a formula of Bultot to compute the motivic zeta function for the toric degeneration of the quartic K3 and its Gross-Siebert mirror dual degeneration. We check for this expli…
An Introduction to Hodge Structures
Sara Angela Filippini, Helge Ruddat, Alan Thompson
We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, whi…
Enumerative aspects of the Gross-Siebert program
Michel van Garrel, D. Peter Overholser, Helge Ruddat
We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and re…
Canonical Coordinates in Toric Degenerations
Helge Ruddat, Bernd Siebert
We prove that the mirror map is trivial for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author. In other words, the natural coordinate…
Perverse Curves and Mirror Symmetry
Helge Ruddat
This work establishes a subtle connection between mirror symmetry for Calabi-Yau threefolds and that of curves of higher genus. The linking structure is what we call a perverse cur…
Skeleta of Affine Hypersurfaces
Helge Ruddat, Nicolò Sibilla, David Treumann +1
A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulatio…
Mirror duality of Landau-Ginzburg models via Discrete Legendre Transforms
Helge Ruddat
We introduce a duality of Landau-Ginzburg models based on the notion of the discrete Legendre transform given by Gross-Siebert. It generalizes the duality used to construct mirrors…