In this paper, we propose an ansatz for defining Gopakumar–Vafa invariants of Calabi–Yau
threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a …

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain
polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a …

We study Hilbert schemes of points on a smooth projective Calabi–Yau 4-fold X. We define
DT 4 invariants by integrating the Euler class of a tautological vector bundle L [n] against the …

Let S be a K3 surface and let E be an elliptic curve. We solve the reduced Gromov–Witten
theory of the Calabi–Yau threefold S * ES× E for all curve classes which are primitive in the …

We construct geometric compactifications of the moduli space F_2d of polarized K3 surfaces
in any degree 2d. Our construction is via KSBA theory, by considering canonical choices of …

Abstract In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective
surfaces is lifted to oriented C^* C∗-equivariant cohomology theories. Here we study the K …

We conjecture that the relative Gromov–Witten potentials of elliptic fibrations are (cycle-
valued) lattice quasi-Jacobi forms and satisfy a holomorphic anomaly equation. We prove …

THE KATZ–KLEMM–VAFA CONJECTURE FOR K3 SURFACES Page 1 Forum of Mathematics,
Pi (2016), Vol. 4, e4, 111 pages doi:10.1017/fmp.2016.2 1 THE KATZ–KLEMM–VAFA …

Abstract In 2008, Klemm–Pandharipande defined Gopakumar–Vafa type invariants of a
Calabi–Yau 4-folds using Gromov–Witten theory. Recently, Cao–Maulik–Toda proposed a …

In this paper we consider three types of localization theorems for algebraic stacks:(i)
Concentration, or cohomological localization. Given an algebraic group acting on a scheme …