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Buryak–Shadrin tautological vanishing conjecture
Let $g,m\geq 0$ , $n\geq 1$ , and let $\textbf{d}=(d_1,\ldots,d_n)\in(\Bbb Z_{\geq 0})^n$ , with $|\textbf{d}|:=d_1+\cdots+d_n$ . For a nondegenerate balanced genus- $g$ stable rooted t…
openintersection-theory moduli-of-curves tautological-relations
03
The identification conjecture for $B^0_{g,\overline{d}}$ and $A^0_{g,\overline{d}}$
Identification conjecture. For any such $g$ , $n$ , and $\overline{d}$ ,
opendouble-ramification-cycles moduli-of-curves tautological-relations
03
The identification conjecture for $B^1_{g,\overline{d}}$ and $A^1_{g,\overline{d}}$
Identification conjecture. For any such $g$ , $n$ , and $\overline{d}$ ,
opendouble-ramification-cycles moduli-of-curves tautological-relations
04
The vanishing conjecture for the classes $B^m_{g,\overline{d}}$
Vanishing conjecture for $B^m_{g,\overline{d}}$ . For any $m\ge 2$ , $g\ge 0$ , $n\ge 1$ , and $\overline{d}$ such that $\sum d_i\ge 2g+m-1$ , one has
openmoduli-of-curves tautological-relations
07
The proportionality conjecture for the sums $P_{n,t}$ and $A_n$
Proportionality conjecture. For every such $n$ , $t$ , and $(a_1,\dots,a_n)$ , one has
opencombinatorics kappa-classes tautological-relations
09

Buryak–Shadrin tautological vanishing conjecture