Algebraic construction of Witten's top Chern class

By Alexander Polishchuk, A. Vaintrob. 2000

118 citations recorded by the source corpus.

We give a construction of Witten's "top Chern class" on the compactified moduli space of curves with higher spin structures and show that it satisfies most of the axioms proposed in math.AG/9905034.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/032c38889f34c947c826a1fa79aab768352c32b0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Dimitri Zvonkine
2. Alexander Polishchuk
3. Tyler Jarvis
4. Y. Ruan

In Geometry and Topology

1. Dimitri Zvonkine
2. L. Spitz
3. Sergey Shadrin
4. Alexander Polishchuk
5. Emanuele Macrì
6. Yuri I. Manin
7. Arend Bayer
8. I. Burban

In Mathematical Physics

1. Dimitri Zvonkine
2. L. Spitz
3. Sergey Shadrin
4. Alexander Polishchuk
5. Yuri I. Manin
6. Emanuele Macrì
7. Arend Bayer
8. Y. Ruan

Citations in the corpus

• Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “R(1)p∗L on M 1/r in a rather involved way (see [33] or [8]).”
• Relations on Mbar_{g,n} via 3-spin structures (2013, unknown): “An algebraic construction was first obtained by Polishchuk and Vain-trob [17] defining W g,n ( a 1 , . . . , a n ) ∈ A ∗ ( M g,n , Q ) as an algebraic cycle class.”
• Witten’s top Chern class on the moduli space of higher spin curves (2002, methodology): “here A∗(Z → X)Q is the bivariant Chow group with rational coefficients. (the original construction given in [1] or [4, Ch. 18] deals with Z-graded complexes). Here we use the following terminology from [9]: (V•,d) is strictly exact if it is exact and im(d) is a subbundle of V•. Note that if a Z/2Z-gra”