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Hodge integrals and Gromov-Witten theory
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of theseExpand
A Conjectural Description of the Tautological Ring of the Moduli Space of Curves
We formulate a number of conjectures giving a rather complete description of the tautological ring of M g and we discuss the evidence for these conjectures.
Relative maps and tautological classes
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stableExpand
Tautological relations and the r-spin Witten conjecture
A geometric interpretation of Y.P. Lee’s algorithm leads to a much simpler proof of the fact that every tautological relation gives rise to a universal relation, and implies that in any semi-simple Gromov–Witten theory where arbitrary correlators can be expressed in genus 0 correlators using only tautology relations, the formal and the geometric Gronov– Witten potentials coincide. Expand
Logarithmic series and Hodge integrals in the tautological ring. With an appendix by Don Zagier.
0.1. Overview. Let Mg be the moduli space of Deligne–Mumford stable curves of genus g ≥ 2. The study of the Chow ring of the moduli space of curves was initiated by Mumford in [Mu]. In the past twoExpand
Complete subvarieties of moduli spaces and the Prym map
We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map and analyze it usingExpand
The Class of the Bielliptic Locus in Genus 3
Let the bielliptic locus be the closure in the moduli space of stable curves of the locus of smooth curves that are double covers of genus 1 curves. In this paper, we compute the class of theExpand
New Trends in Algebraic Geometry: Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians
We describe algorithms for computing the intersection numbers of divisors and of Chern classes of the Hodge bundle on the moduli spaces of stable pointed curves. We also discuss the implementationsExpand
Siegel modular forms of degree three and the cohomology of local systems
We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space $$\mathcal{A }_3$$ of principally polarized abelianExpand
Siegel modular forms of genus 2 and level 2: Cohomological computations and conjectures
We study the cohomology of certain local systems on moduli spaces of principally polarized abelian surfaces with a level 2 structure. The trace of Frobenius on the alternating sum of the \'etaleExpand