We characterize transversality, non-transversality properties on the moduli space of genus 0 stable maps to a rational projective surface. If a target space is equipped with a real structure, i.e, anti-holomorphic involution, then the results have real enumerative applications. Firstly, we can define a real version of Gromov-Witten invariants. Secondly, we can prove the invariance of Welschinger's invariant in algebraic geometric category.
Gromov-Witten invariant, enumerative invariant, transversality, intersection multiplicity, real structure
KWON, SEONGCHUN (2008) "Real Gromov-Witten Invariants on the Moduli Space of Genus 0 Stable Maps to a Smooth Rational Projective Space," Turkish Journal of Mathematics: Vol. 32: No. 2, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol32/iss2/4