4 papers · 1 filter
The dimension threshold for Batyrev's non-negativity conjecture on stringy Hodge numbers
Jiahui Huang, Matthew Satriano
Batyrev's non-negativity conjecture has been a major guiding conjecture in mirror symmetry, motivic integration, and the McKay correspondence. We show the conjecture is true in dim…
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…