The log Grothendieck ring of varieties
Andreas Gross, Leo Herr, David Holmes, Pim Spelier, Jesse Vogel

TL;DR
This paper introduces a Grothendieck ring for log schemes, adding a new class, and addresses the challenges in defining log Hodge numbers, proposing a viable alternative.
Contribution
It extends the Grothendieck ring framework to log schemes and provides a new approach to defining log Hodge numbers.
Findings
Defined a Grothendieck ring for log schemes with an additional class P
Identified issues with naive log Hodge number definitions
Proposed an alternative definition for log Hodge numbers
Abstract
We define a Grothendieck ring of varieties for log schemes. It is generated by one additional class ``'' over the usual Grothendieck ring. We show the na\"ive definition of log Hodge numbers does not make sense for all log schemes. We offer an alternative that does.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation
