Matching Tag: holomorphic-anomaly
For a Calabi–Yau A ∞ A_\infty A ∞
For g ≥ 0 g\geq 0 g ≥ 0 n ≥ 1 n\geq 1 n ≥ 1 Z g ; n ( q ) : = ∑ d N g , d ; n q d Z_{g;n}(q):=\sum_dN_{g,d;n}q^d Z g ; n ( q ) := ∑ d N g , d ; n q d N g , d ; n : = ∑ ( β , σ ) = d , ( β , F ) = n N g ( β ) N_{g,d;n}:=\sum_{(\beta,\sigma)=d,\,(\beta,F)=n}N_g(\beta) N g , d ; n := ∑ ( β , σ ) = d , ( β , F ) = n N g ( β ) E 2 ( q ) , E 4 ( q ) , E 6 ( q ) E_2(q),E_4(q),E_6(q) E 2 ( q ) , E 4 ( q ) , E 6 ( q )
Let F ~ g B \widetilde{\mathcal{F}}^{\mathsf{B}}_g F g B g g g T = I 1 Q ( q ) / I 0 Q ( q ) T=I^{\mathsf{Q}}_1(q)/I^{\mathsf{Q}}_0(q) T = I 1 Q ( q ) / I 0 Q ( q )
Let K P 3 K\mathbb{P}^3 K P 3 T = I 1 K P 3 ( q ) T=I^{K\mathbb{P}^3}_1(q) T = I 1 K P 3 ( q ) F g , a + b S Q a , b \mathcal{F}^{\mathsf{SQ}}_{g,a+b}a,b F g , a + b SQ a , b
Let K P 2 K\mathbb{P}^2 K P 2 T = I 1 K P 2 ( q ) T=I^{K\mathbb{P}^2}_1(q) T = I 1 K P 2 ( q ) F g S Q \mathcal{F}^{\mathsf{SQ}}_g F g SQ g g g
Let K P 2 K\mathbb{P}^2 K P 2 q q q T = I 1 K P 2 ( q ) T=I^{K\mathbb{P}^2}_1(q) T = I 1 K P 2 ( q ) Q ( q ) = exp ( T ) Q(q)=\exp(T) Q ( q ) = exp ( T )
