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math.AG2024
On sums of Betti numbers of affine varieties
Dingxin Zhang
We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its -adic Betti numbers does not exceed $2(N + 1)^{2N +1}(…
math.AG2024
Generic Triviality of Automorphism Groups of Complete Intersections
Renjie Lyu, Dingxin Zhang
We prove in most cases that a general smooth complete intersection in the projective space has no non-trivial automorphisms.