Invariance of tautological equations I: conjectures and applications

Y.-P. Lee

Journal of the European Mathematical Society (2008)

  • Volume: 010, Issue: 2, page 399-413
  • ISSN: 1435-9855

Abstract

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The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to two.

How to cite

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Lee, Y.-P.. "Invariance of tautological equations I: conjectures and applications." Journal of the European Mathematical Society 010.2 (2008): 399-413. <http://eudml.org/doc/277765>.

@article{Lee2008,
abstract = {The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to two.},
author = {Lee, Y.-P.},
journal = {Journal of the European Mathematical Society},
keywords = {Chow rings; tautological rings; tautological equations; tautological rings; Chow rings; tautological equations},
language = {eng},
number = {2},
pages = {399-413},
publisher = {European Mathematical Society Publishing House},
title = {Invariance of tautological equations I: conjectures and applications},
url = {http://eudml.org/doc/277765},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Lee, Y.-P.
TI - Invariance of tautological equations I: conjectures and applications
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 399
EP - 413
AB - The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite-dimensional linear algebra. Other applications include the proofs of Witten’s conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to two.
LA - eng
KW - Chow rings; tautological rings; tautological equations; tautological rings; Chow rings; tautological equations
UR - http://eudml.org/doc/277765
ER -

Citations in EuDML Documents

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  1. Sergey Shadrin, Dimitri Zvonkine, A group action on Losev-Manin cohomological field theories
  2. Tom Coates, Yongbin Ruan, Quantum Cohomology and Crepant Resolutions: A Conjecture
  3. M. Hairer, N. S. Pillai, Ergodicity of hypoelliptic SDEs driven by fractional brownian motion
  4. Carel Faber, Sergey Shadrin, Dimitri Zvonkine, Tautological relations and the r -spin Witten conjecture
  5. J. Šnupárková, Weak solutions to stochastic differential equations driven by fractional Brownian motion

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