## Advances in Theoretical and Mathematical Physics

### Virtual class of zero loci and mirror theorems

#### Abstract

Let $Y$ be the zero loci of a regular section of a convex vector bundle $E$ over $X$. We provide a proof of a conjecture of Cox, Katz and Lee for the virtual class of the genus zero moduli of stable maps to $Y$. This in turn yields the expected relationship between Gromov-Witten theories of $Y$ and $X$ which together with Mirror Theorems allows for the calculation of enumerative invariants of $Y$ inside of $X$.

#### Article information

Source
Adv. Theor. Math. Phys., Volume 7, Number 6 (2003), 1103-1115.

Dates
First available in Project Euclid: 21 June 2004

https://projecteuclid.org/euclid.atmp/1087840805

Mathematical Reviews number (MathSciNet)
MR2061644

Zentralblatt MATH identifier
1078.14080

#### Citation

Elezi, Artur; Luo, Feng. Virtual class of zero loci and mirror theorems. Adv. Theor. Math. Phys. 7 (2003), no. 6, 1103--1115. https://projecteuclid.org/euclid.atmp/1087840805