The Canonical Class of $\overline{M}_{0,n}(P^r,d)$ And Enumerative Geometry

TL;DR

This paper revises the canonical class formulas for moduli spaces of stable maps to projective space, correcting an earlier error in the arithmetic genus calculation while confirming other invariants remain unchanged.

Contribution

It provides corrected formulas for the canonical class of _{0,n}(P^r,d), refining previous results and ensuring accuracy in enumerative geometry applications.

Findings

Corrected arithmetic genus formula

Confirmed unchanged geometric genus

Maintained existing canonical class formulas

Abstract

D. Abramovich found an error in the singularity analysis in the first posting of this paper affecting one formula (Thanks Dan).The error has been corrected. Only the arithmetic genus formula has changed. The geometric genus and all the canonical class formulas are the same.