arXiv subjects

Felix Thimm

Publications and source records attributed to Felix Thimm.

5 recordsLinked to original sources

arXiv2026

Universal Curve Counting in Calabi-Yau 4-folds

Recently, Pardon introduced a universal curve counting framework, which allows him to show that curve counting on 3-folds is "generated" by local curves (in a precise sense). We implement this universal curve counting program for Calabi-Yau 4-folds, where a significant technical difficulty comes from the dependence of the virtual dimension on the genus, which leads to more complicated generators than just local curves. Our main techniques are combinations of deformation-theoretic and homotopy-theoretic methods with an adaptation of Pardon's generic transversality results, which allow us to establish a full set of (computable) generators for CY4 curve counting. As a result, we prove (a slight correction of) the Gromov-Witten/Pandharipande-Thomas correspondence with primary descendents for CY4-folds, formulated by Cao, Maulik, and Toda. From this, we additionally obtain integrality of Gopakumar-Vafa style invariants for CY4-folds, as conjectured by Klemm-Pandharipande.

math.AG↗

arXiv2026

Wall-crossing for equivariant DT4 invariants

We prove the wall-crossing formula conjectured by Gross--Joyce--Tanaka for equivariant enumerative invariants of CY4 categories equipped with framing functors. We also establish a version for stable pairs with fixed-determinant obstruction theories, as used in earlier applications by the first-named author. The main technical ingredient, which we develop in this work, is a construction of well-behaved CY4 pullback virtual classes using Jouanolou devices.

math.AG↗

arXiv2025

Wall-crossing for invariants of equivariant 3CY categories

We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wall-crossing framework arXiv:2111.04694, using the authors' symmetrized pullback technique to preserve the symmetry of the (almost-perfect) obstruction theories throughout. As an application, we define and study wall-crossings of simple type between operational equivariant Donaldson--Thomas (DT), Pandharipande--Thomas (PT), and Bryan--Steinberg (BS) vertices. In particular, we give an explicit DT/PT descendent vertex correspondence in the Calabi--Yau limit. As another application, we construct and prove wall-crossing formulas for operational refined semistable Vafa--Witten invariants.

math.AG↗

arXiv2024

K-Theoretic Donaldson-Thomas Theory of $[\mathbb{C}^2/μ_r]\times\mathbb{C}$ and Factorization

We compute the equivariant K-theoretic Donaldson--Thomas invariants of $[\mathbb{C}^2/μ_r]\times \mathbb{C}$ using factorization and rigidity techniques. For this, we develop a generalization of Okounkov's factorization technique that applies to Hilbert schemes of points on orbifolds. We show that the (twisted) virtual structure sheaves of Hilbert schemes of points on orbifolds satisfy the desired factorization property. We prove that the generating series of Euler characteristics of such factorizable systems are the plethystic exponential of a simpler generating series. For $[\mathbb{C}^2/μ_r]\times \mathbb{C}$, the computation is then completed by a rigidity argument, involving an equivariant modification of Young's combinatorial computation of the corresponding numerical Donaldson-Thomas invariants.

math.AG↗

arXiv2023

The 3-fold K-theoretic DT/PT vertex correspondence holds

We prove the 3-fold DT/PT correspondence for K-theoretic vertices via wall-crossing techniques. We provide two different setups, following Mochizuki and following Joyce; both reduce the problem to q-combinatorial identities on word rearrangements. An important technical step is the construction of symmetric almost-perfect obstruction theories (APOTs) on auxiliary moduli stacks, e.g. master spaces, from the symmetric DT or PT obstruction theory. For this, we introduce symmetrized pullbacks of symmetric obstruction theories along smooth morphisms of Artin stacks.

math.AG↗