# Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds

@article{Katz2004GromovWittenGA, title={Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds}, author={Sheldon Katz}, journal={arXiv: Algebraic Geometry}, year={2004} }

Gromov-Witten, Gopakumar-Vafa, and Donaldson-Thomas invariants of Calabi-Yau threefolds are compared. In certain situations, the Donaldson-Thomas invariants are very easy to handle, sometimes easier than the other invariants. This point is illustrated in several ways, especially by revisiting computations of Gopakumar-Vafa invariants by Katz, Klemm, and Vafa in a rigorous mathematical framework. This note is based on my talk at the 2004 Snowbird Conference on String Geometry.

## 27 Citations

### Super-rigid Donaldson-Thomas Invariants

- Mathematics
- 2006

We solve the part of the Donaldson-Thomas theory of Calabi-Yau threefolds which comes from super-rigid rational curves. As an application, we prove a version of the conjectural…

### THE GROMOV–WITTEN AND DONALDSON–THOMAS CORRESPONDENCE FOR TRIVIAL ELLIPTIC FIBRATIONS

- Mathematics
- 2006

We study the Gromov–Witten and Donaldson–Thomas correspondence conjectured in [16, 17] for trivial elliptic fibrations. In particular, we verify the Gromov–Witten and Donaldson–Thomas correspondence…

### Stability conditions and curve counting invariants on Calabi–Yau 3-folds

- Mathematics
- 2012

The purpose of this paper is twofold: first we give a survey on the recent developments of curve counting invariants on Calabi-Yau 3-folds, e.g. Gromov-Witten theory, Donaldson-Thomas theory and…

### Khovanov-Rozansky Homology and Topological Strings

- Mathematics
- 2005

We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to…

### Elliptic Calabi-Yau threefolds over a del Pezzo surface

- Mathematics
- 2013

We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a del Pezzo surface of…

### Towards refining the topological strings on compact Calabi-Yau 3-folds

- Mathematics
- 2020

We make a proposal for calculating refined Gopakumar-Vafa numbers (GVN) on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. The key examples are smooth elliptic…

### Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections

- Mathematics
- 2005

We present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus…

### On certain moduli spaces of ideal sheaves and Donaldson-Thomas invariants

- Mathematics
- 2005

We determine the structure of certain moduli spaces of ideal sheaves by generalizing an earlier result of the first author. As applications, we compute the (virtual) Hodge polynomials of these moduli…

### Stable pairs on local $K3$ surfaces

- Mathematics
- 2011

We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes…

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