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math.AG2026
Asymptotic Betti bounds for hypersurfaces in a singular variety
Xuanyu Pan, Dingxin Zhang, Xiping Zhang
We show that for any degree hypersurface in a possibly singular projective variety , the total Betti number of is bounded by $3\text{d…
math.AG2017
1-Cycles on Fano varieties
Cristian Minoccheri, Xuanyu Pan
We prove results about 1-cycles on certain Fano varieties using techniques that rely on rational curves. Firstly, we show that Fano weighted complete intersections with index bigge…