中央研究院數學研究所

Algebraic Hyperbolicity of Very General Vanishing Loci in Homogeneous Varieties

2026/09/30 (Wed.) 10:30~11:30

日期 : 2026/09/30 (Wed.) 10:30~11:30
地點 : 中研院數學所 638研討室 (台大校區)
主講人 : 戴碧寬 (Penn State University)
籌辦人 : 鄭日新 (AS)
演講摘要 : A variety $X$ is said to be algebraically hyperbolic if there exist an ample divisor H and a positive number $\epsilon$ such that for every integral curve $C$ on $X$ we have $2g(C)-2\ge\epsilon\deg(HC)$. Algebraic hyperbolicity, introduced by Demailly, is the algebraic analogue of Kobayashi and Brody hyperbolicity. Demailly conjectured that for a smooth projective complex variety, these notions of hyperbolicity are equivalent. In this talk, we discuss the algebraic hyperbolicity of certain subvarieties of homogeneous varieties, building on the techniques introduced by Coskun-Riedl, Yeong and Mioranci. This generalizes earlier known results for hypersurfaces to higher codimensions. In particular, we observe that if $X=X_1\cap\cdots\cap X_k$ is a very general complete intersection of degree $d_j$ hypersurfaces $X_j$ in $\mathbb{P}^n$ with $k\le n-2$, then $X$ is algebraically hyperbolic if $\sum d_j\ge 2n-k$, and $X$ is not algebraically hyperbolic if $\sum d_j\le 2n-k-2$.