## 2 Citations

### Irreducible Contact Curves via Graph Stratification

- Mathematics
- 2022

. We prove that the moduli space of contact stable maps to P 2 n +1 of degree d admits a stratiﬁcation parameterized by graphs. We use it to determine the number of irreducible rational contact…

### Enumeration of Rational Contact Curves via Torus Actions

- MathematicsMichigan Mathematical Journal
- 2022

We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerative. Also, we use…

## References

SHOWING 1-10 OF 36 REFERENCES

### Enumeration of Rational Contact Curves via Torus Actions

- MathematicsMichigan Mathematical Journal
- 2022

We prove that some Gromov-Witten numbers associated to rational contact (Legendrian) curves in any contact complex projective space with arbitrary incidence conditions are enumerative. Also, we use…

### Localization of virtual classes

- Mathematics
- 1997

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of…

### Bott’s formula and enumerative geometry

- Mathematics
- 1994

We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic…

### Generating Functions in Algebraic Geometry and Sums Over Trees

- Mathematics
- 1995

We calculate generating functions for the Poincare polynomials of moduli spaces of pointed curves of genus zero and of Configuration Spaces of Fulton and MacPherson. We also prove that contributions…

### A recursive formula for osculating curves

- Mathematics
- 2020

Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is…

### Topological field theory and rational curves

- Mathematics
- 1993

We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear σ-model and…

### Quantum intersection rings

- Mathematics
- 1994

Within the broadly defined subject of topological field theory E. Witten suggested in [1] to study generalized “intersection numbers” on a compactified moduli space \({\bar M_{g,n}}\) of Riemann…

### Absolute and relative Gromov-Witten invariants of very ample hypersurfaces

- Mathematics
- 1999

For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms.…

### Symplectic enumeration

- Mathematics
- 2011

Every complex projective space of odd dimension carries a natural contact structure. We give first steps towards the enumeration of curves in ℙ3 tangent to the contact structure. Such a curve is…

### Rational curves on Calabi-Yau threefolds: Verifying mirror symmetry predictions

- MathematicsJ. Symb. Comput.
- 2016