NOETHER-LEFSCHETZ THEORYAND THE YAU-ZASLOW CONJECTURE

摘要

Yau-Zaslow conjecture. Let S be a nonsingular projective K3 surface, and let ∈ Pic(S) = H~2 (S, Z) n H~(1,1)(S,C)be a nonzero effective curve class. The moduli space M_0(S, β) of genus 0 stable maps (with no marked points) has the expected dimension (M 0(S, /3)) = fci(S) dime (S) — 3 = —1.Hence, the virtual class [M o(S, O)]"Z' vanishes, and the standard Gromov-Witten theory is trivial.