中国科学院数学与系统科学研究院

数学研究所

学术报告

代数几何研讨班

报告人: 徐言 讲师（南开大学）

题  目：Fano 3-folds and classification of constantly curved holomorphic 2-spheres of degree 6 in the complex Grassmannian G(2,5)

时  间：2024.11.05（星期二）14：00-15：00

地  点：思源楼S615

摘  要：Up to now the only known constantly curved sextic curve, i.e., holomorphic 2-sphere of degree 6, in the complex G(2,5) has been the first associated curve of the Veronese curve of degree 4, which indicates that such curves are rare to find. We prove through elaborate PSL2-transvectant and engaged unitary analyses that, up to the ambient unitary equivalence, the moduli space of constantly curved sextic curves in G(2,5) that are GL(5,C)-equivalent to those in V5 ramified at the PSL2-invariant 1-dimensional singular locus somewhere, is semialgebraic of dimension 2 all members of which barring the above Veronese curve are nonhomogeneous. Many explicit examples can be constructed.