2 citations · 4 across the 6 of their papers we have counts for
6 papers
Waring Problem for Matrices over Finite Fields
Krishna Kishore, Adrian Vasiu, Sailun Zhan
We prove that for all integers , , and , every matrix in is a sum of two kth powers: $M_m(\mathbb F_q)=\{A^k+B^k|A,B\in M_…
Punctual Hilbert schemes of points of in the Grothendieck group of varieties
Sailun Zhan
We give an explicit stratification of the punctual Hilbert schemes of points of with respect to -dimensional partitions in the Grothendieck group of varie…
Hilbert schemes of points on smooth projective surfaces and generalized Kummer varieties with finite group actions
Sailun Zhan
Göttsche and Soergel gave formulas for the Hodge numbers of Hilbert schemes of points on a smooth algebraic surface and the Hodge numbers of generalized Kummer varieties. When a sm…
Shimura Varieties, Kummer Varieties, and Rational Curves
Bo-Hae Im, Michael Larsen, Sailun Zhan
For a very general product of seven or more elliptic curves, every rational curve on the Kummer variety of projects trivially onto the Kummer variety of at least one of its…
Monodromy of rational curves on K3 surfaces of low genus
Sailun Zhan
In many situations, the monodromy group of enumerative problems will be the full symmetric group. In this paper, we study a similar phenomenon on the rational curves in $|\mathcal{…
Counting rational curves on K3 surfaces with finite group actions
Sailun Zhan
Göttsche gave a formula for the dimension of the cohomology of Hilbert schemes of points on a smooth projective surface . When admits an action by a finite group , we des…