Tautological equations in genus 2 via invariance conjectures
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
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arXiv subjects
Y. -P. Lee
Publications and source records attributed to Y. -P. Lee.
Tautological equation in \bar{M}_{3,1} via invariance conjectures
A new tautological equation of $\Mbar_{3,1}$ in codimension 3 is derived and proved, using the invariance condition explained in earlier works.
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Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional linear algebra. Other applications are also indicated.
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Orbifold Euler characteristics of universal cotangent line bundles on $\bar{M}_{1,n}$
A scheme of computing $χ(\mbar_{1,n}, L_1^{\otimes d_1}\otimes ... \otimes L_n^{\otimes d_n})$ is given. Here $\mbar_{1,n}$ is the moduli space of $n$-pointed stable curves of genus one and $L_i$ are the universal cotangent line bundles defined by $x_i^*(ω_{C/M})$, where $C \to \mbar_{1,n}$ is the universal curve, $ω_{C/M}$ the relative dualizing sheaf and $x_i$ the marked point. This work is a sequel to \cite{YL1}.
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Witten's conjecture and Virasoro conjecture for genus up to two
This is an expository paper based on the results in [12] and [16]. The main goal is to prove the following two conjectures for genus up to two. (1) Witten's conjecture on the relations between higher spin curves and Gelfand-Dickey Hierarchies. (2) Virasoro conjecture for conformal semisimple Frobenius manifolds.
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Witten's conjecture, Virasoro conjecture, and invariance of tautological equations
The main goal of this paper is to prove the following two conjectures for genus up to two: 1. Witten's conjecture on the relations between higher spin curves and Gelfand--Dickey hierarchy. 2. Virasoro conjecture for target manifolds with conformal semisimple Frobenius manifolds. The main technique used in the proof is the invariance of tautological equations under loop group action.
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A reconstruction theorem in quantum cohomology and quantum K-theory
A reconstruction theorem for genus 0 gravitational quantum cohomology and quantum K-theory is proved. A new linear equivalence in the Picard group of the moduli space of genus 0 stable maps relating the pull-backs of line bundles from the target via different markings is used for the reconstruction result. Examples of calculations in quantum cohomology and quantum K-theory are given.
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