论文标题
M-Curves的双曲线割线
Hyperbolic Secant Varieties of M-Curves
论文作者
论文摘要
我们将曲线的几何形状与实际代数几何形状中的双曲线概念联系起来。双曲线变化是一个真正的代数品种，它（尤其是）接收到一个真实的纤维形态，其尺寸等于多样性的尺寸。我们研究了在承认实际代数裁决的高空曲面的情况下特别感兴趣的双曲线品种。本文的中心部分与真实代数曲线的距离距离品种有关，其中真实基因座具有最大的连接组件数量，该组件由曲线的属确定。对于椭圆形的曲线，我们进一步获得了双曲线脱毛性超曲面的明确的对称决定性表示，这意味着在这些超曲面上存在对称对称的Ulrich滑轮。
We relate the geometry of curves to the notion of hyperbolicity in real algebraic geometry. A hyperbolic variety is a real algebraic variety that (in particular) admits a real fibered morphism to a projective space whose dimension is equal to the dimension of the variety. We study hyperbolic varieties with a special interest in the case of hypersurfaces that admit a real algebraic ruling. The central part of the paper is concerned with secant varieties of real algebraic curves where the real locus has the maximal number of connected components, which is determined by the genus of the curve. For elliptic normal curves, we further obtain definite symmetric determinantal representations for the hyperbolic secant hypersurfaces, which implies the existence of symmetric Ulrich sheaves of rank one on these hypersurfaces.
