Qizheng Yin

Some remarks on modified diagonals

We prove a number of basic vanishing results for modified diagonal classes. We also obtain some sharp results for modified diagonals of curves and abelian varieties, and we prove a conjecture of O’...

Cycles on curves and Jacobians: a tale of two tautological rings

We connect two notions of tautological ring: one for the moduli space of curves (after Mumford, Faber, etc.), and the other for the Jacobian of a curve (after Beauville, Polishchuk, etc.). The motivic Lefschetz decomposition on the Jacobian side produces relations between tautological classes, leading to results about Faber’s Gorenstein conjecture on the curve side. We also relate certain Gorenstein properties on both sides and verify them for small genera. Further, we raise the question whether all tautological relations are motivic, giving a possible explanation why the Gorenstein properties may not hold.