A note on congruences for theta divisors
Franziska Heinloth
TL;DR
This paper discusses the relationship between classes of theta divisors on abelian varieties in the Grothendieck ring, showing they may not be congruent modulo the affine line class.
Contribution
It provides a counterexample to the assumption that classes of two theta divisors are always congruent modulo the affine line in the Grothendieck ring.
Findings
Classes of two theta divisors can differ modulo the affine line.
Counterexample challenges previous conjectures.
Highlights complexities in the Grothendieck ring of varieties.
Abstract
The classes of two theta divisors on an abelian variety in the naive Grothendieck ring of varieties need not be congruent modulo the class of the affine line.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications