Towards the leading constant in Stacky Manin’s conjecture

Abstract: Manin’s conjecture is a famous conjecture in arithmetic geometry, predicting asymptotically the number of rational points of bounded height on Fano varieties.

In a breaking recent advance, the researcher and Yasuda have [Darda-Yasuda]extended it to stacks, which explains Malle’s conjecture on the number of Galois extensions with fixed Galois group of bounded discriminant. The leading constant in the asymptotic formula, however, remains unknown. A reason for this is that we still have very little verified examples of Stacky Manin’s conjecture.

In this proposal, we identify a class of stacks for which the conjecture seems to be approachable, namely, the class of smooth complete intersections in weighted projective stacks which enjoys rich geometric properties.

We then plan to analyze the obtained constant, compare it with existing examples, to guess the shape in the general case.