论文标题
FANO 3倍和不断弯曲的全体形态的分类$ 2 $ -SPHERES学位$ 6 $在复杂的Grassmannian $ G（2,5）$中
Fano 3-folds and classification of constantly curved holomorphic $2$-spheres of degree $6$ in the complex Grassmannian $G(2,5)$
论文作者
论文摘要
到目前为止，唯一已知的不断弯曲的六曲线，即6级的全体形态2杆，在复杂的$ g（2,5）$中是4度的Veronese曲线的第一条相关曲线，这表明这种曲线很少见。 Exploring the rich interplay between the ramification of harmonic sequences in differential geometry and algebro-geometric properties of projectively equivalent Fano 3-folds of index 2 and degree 5, we invoke the moduli space structure of sextic curves in the Fano 3-fold often referred to as $V_5$ to confirm the rarity of constancy of curvature, by establishing that the harmonic sequence of a generic sextic curve in $ g（2，5）$完全不受影响。本文提议从Galois的角度进行调查，以$ G（2，5）$中的非元素六曲线之间的曲率稳定性出现。我们通过精美的$ psl_2 $ - 翻译和参与的单一分析证明，直到环境单一的等价性，这是$ g（2,5）$ $ g（2,5）$ gl（5，5，{\ mathbb c}）$ fly g（2,5）$的模量空间，{\ mathbb c}）$ - 在$ v_5 $ ramimient $ ps y-ps y-pslim y-pslim y-pslim y-pslim y-p y-pslim-ramimient yim y-pslim y-pslim y-p lam ramimient yound $ - 在某个地方，是维度2的半格言。2所有成员的所有成员都不均匀。可以构建许多明确的例子。
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. Exploring the rich interplay between the ramification of harmonic sequences in differential geometry and algebro-geometric properties of projectively equivalent Fano 3-folds of index 2 and degree 5, we invoke the moduli space structure of sextic curves in the Fano 3-fold often referred to as $V_5$ to confirm the rarity of constancy of curvature, by establishing that the harmonic sequence of a generic sextic curve in $G(2, 5)$ is totally unramified. This paper proposes to investigate from the Galois viewpoint the way ramification can appear in relation to the constancy of curvature among nongeneric sextic curves in $G(2, 5)$. We prove through elaborate $PSL_2$-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 $GL(5,{\mathbb C})$-equivalent to those in $V_5$ ramified at the $PSL_2$-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.
