Moduli of weighted stable maps and their gravitational descendants
Guy, Gary Michael
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We study the intersection theory on the moduli spaces of maps of n-pointed curves f : (C, s1, . . . sn) → V which are stable with respect to the weight data (a1, . . . , an), 0 ≤ ai ≤ 1. After describing the structure of these moduli spaces, we define an analog of the gravitational descendants from Gromov-Witten theory using them. We state and prove the equality of some of these descendants to previous numerical invariants of Miller, Morita and Mumford as well as those of Graber, Kock, and Pandharipande. We then prove a formula describing the way each descendant changes as we vary the weights. Finally, we state and prove several nice relationships among these descendants including generalizations of the string, dilaton, and divisor equation.