6 papers
A complete classification of negative stringy Hodge numbers
Jiahui Huang, Matthew Satriano
The stringy -function is a fundamental invariant of varieties with log-terminal singularities, which was introduced by Batyrev as a singular analogue of the Hodge--Deligne polyn…
McKay correspondence for linearly reductive finite group schemes in positive characteristic
Matthew Satriano, Jeremy Usatine
We obtain a motivic and a cohomological McKay correspondence for finite linearly reductive group schemes in arbitrary characteristic. In particular, we prove that if is a finit…
A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers
Matthew Satriano, Jeremy Usatine
Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integ…
-Equivalence and Integral Cohomology
Matthew Satriano, Evan Sundbo
We introduce an integral version of the Hodge polynomial, which encodes the integral cohomology of smooth projective varieties. We prove it extends to a function which is well-defi…
On combinatorial algebras generated by three commuting matrices
Ron Cherny, Tam An Le Quang, Matthew Satriano
Motzkin and Taussky (and independently, Gerstenhaber) proved that the unital algebra generated by a pair of commuting matrices over a field has dimension at most . S…
On the algebra generated by three commuting matrices: combinatorial cases
Ron Cherny, Matthew Satriano, Yohan Song
Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting matrices over a field has dimension at most . It is an open problem whether the…