Felix Janda
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View article: Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks
Gromov--Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks Open
In this paper we compute genus 0 orbifold Gromov--Witten invariants of Calabi--Yau threefold complete intersections in weighted projective stacks, regardless of convexity conditions. The traditional quantumn Lefschetz principle may fail ev…
View article: Structure results for torus fixed loci
Structure results for torus fixed loci Open
Motivated by localization theorems on moduli spaces, we prove a structural classification of Deligne-Mumford stacks with an action of a torus where the induced action on the coarse moduli space is trivial. We also establish a general local…
View article: Universal equations for higher genus Gromov-Witten invariants from Hodge integrals
Universal equations for higher genus Gromov-Witten invariants from Hodge integrals Open
We establish new universal equations for higher genus Gromov-Witten invariants of target manifolds, by studying both the Chern character and Chern classes of the Hodge bundle on the moduli space of curves. As a consequence, we find new pus…
View article: Gromov--Witten invariants with naive tangency conditions
Gromov--Witten invariants with naive tangency conditions Open
We introduce Gromov-Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov-Witten invariants with naive tangency conditions in terms of descen…
View article: Topological Recursion Relations from Pixton’s Formula
Topological Recursion Relations from Pixton’s Formula Open
We prove that every degree-g polynomial in the $\\psi$-classes on\n$\\overline{\\mathcal M}_{g, n}$ can be expressed as a sum of tautological\nclasses supported on the boundary with no $\\kappa$-classes. Such equations,\nwhich we refer to …
View article: Punctured logarithmic R-maps
Punctured logarithmic R-maps Open
In this paper, we develop the theory of punctured R-maps as a crucial component of logarithmic gauged linear sigma models (log GLSM). A punctured R-map is a punctured map in the sense of ACGS, further twisted by the sheaf of differentials …
View article: Virtual cycles of stable (quasi-)maps with fields
Virtual cycles of stable (quasi-)maps with fields Open
We generalize the results of Chang-Li, Kim-Oh and Chang-Li on the moduli of\n$p$-fields to the setting of (quasi-)maps to complete intersections in\narbitrary smooth Deligne-Mumford stacks with projective coarse moduli. In\nparticular, we …
View article: Socle pairings on tautological rings
Socle pairings on tautological rings Open
We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes suppor…
View article: Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds Open
There is a set of remarkable physical predictions for the structure of BCOV's higher genus B-model of mirror quintic 3-folds which can be viewed as conjectures for the Gromov-Witten theory of quintic 3-folds. They are (i) Yamaguchi--Yau's …
View article: Pixton’s double ramification cycle relations
Pixton’s double ramification cycle relations Open
We prove a conjecture of Pixton, namely that his proposed formula for the\ndouble ramification cycle on Mbar_{g,n} vanishes in codimension beyond g. This\nyields a collection of tautological relations in the Chow ring of Mbar_{g,n}.\nWe de…
View article: Gromov–Witten Theory of Target Curves and the Tautological Ring
Gromov–Witten Theory of Target Curves and the Tautological Ring Open
In the Gromov–Witten theory of a target curve, we consider descendent integrals against the virtual fundamental class relative to the forgetful morphism to the moduli space of curves. We show that cohomology classes obtained in this way li…
View article: A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds Open
We derive a closed formula for the generating function of genus two Gromov-Witten invariants of quintic 3-folds and verify the corresponding mirror symmetry conjecture of Bershadsky, Cecotti, Ooguri and Vafa.
View article: Higher-genus wall-crossing in the gauged linear sigma model
Higher-genus wall-crossing in the gauged linear sigma model Open
We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear sigma model as the stability parameter varies, without assuming factorization properties of the virtual class. We implement this technique explicitl…
View article: Powers of the Theta Divisor and Relations in the Tautological Ring
Powers of the Theta Divisor and Relations in the Tautological Ring Open
We show that the vanishing of the $(g+1)$-st power of the theta divisor in the cohomology and Chow rings of the universal abelian variety implies, by pulling back along a collection of Abel-Jacobi maps, the vanishing results in the tautolo…
View article: Relations on Mgn via equivariant Gromov-Witten theory of P1
Relations on Mgn via equivariant Gromov-Witten theory of P1 Open
We give a proof of Pixton's generalized Faber-Zagier relations in the\ntautological Chow ring of $\\overline M_{g,n}$. The strategy is very similar to\nthe work of Pandharipande-Pixton-Zvonkine, who have given a proof of the same\nresult i…
View article: Topological recursion relations from Pixton's formula
Topological recursion relations from Pixton's formula Open
We prove that every degree-g polynomial in the $ψ$-classes on $\overline{\mathcal M}_{g, n}$ can be expressed as a sum of tautological classes supported on the boundary with no $κ$-classes. Such equations, which we refer to as topological …
View article: Higher-genus quasimap wall-crossing via localization
Higher-genus quasimap wall-crossing via localization Open
We give a new proof of Ciocan-Fontanine and Kim's wall-crossing formula relating the virtual classes of the moduli spaces of $ε$-stable quasimaps for different $ε$ in any genus, whenever the target is a complete intersection in projective …
View article: Double ramification cycles on the moduli spaces of curves
Double ramification cycles on the moduli spaces of curves Open
Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to th…