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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Bernstein Theorem of Affine Maximal Hypersurface
仿射 极大超曲面 伯恩斯坦定理
2023/4/13
Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for enti...
Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface
Nonpositively curved manifolds prescribed nonpositively curved hypersurface Differential Geometry
2012/6/9
We use pinched smooth hyperbolization to show that every closed, nonpositively curved $n$-dimensional manifold $M$ can be embedded as a totally geodesic submanifold of a closed, nonpositively curved $...
What is the total Betti number of a random real hypersurface?
Betti number random real hypersurface Algebraic Geometry
2011/9/2
Abstract: We bound from above the expected total Betti number of a high degree random real hypersurface in a smooth real projective manifold. This upper bound is deduced from the equirepartition of cr...
The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring
Almost Complete Intersection Enumeration of Plane Partitions
2011/1/18
Let k be a field. For each pair of positive integers (n,N), we resolve Q = R/(xN, yN, zN) as a module over the ring R = k[x, y, z]/(xn +yn + zn). Write N in the form N = an + r for integers a and r.
Singular set of a Levi-flat hypersurface is Levi-flat
Singular set Levi-flat hypersurface Levi-flat
2011/3/1
We study the singular set of a singular Levi-flat real-analytic hypersurface.We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense.We also show that if the singul...
Intrinsic Equations for a Relaxed Elastic Line on an Oriented Hypersurface in the Minkowski Space Rn1
Elastic line Minkowski space
2010/3/1
We gived the intrinsic equations for a relaxed elastic line on an oriented surface in {\Bbb {R}}13 ([1],[2]). In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriente...
Smooth hypersurface sections containing a given subscheme over a finite field
Smooth hypersurface sections given subscheme finite field
2011/1/17
et Fq be a finite field of q = pa elements. Let X be a smooth quasi-projective subscheme
of Pn of dimension m ≥ 0 over Fq. N. Katz asked for a finite field analogue of the Bertini
smoothness theorem...
The Pitch and the Angle of Pitch of a Closed Nonnull Ruled Hypersurface Whose Generator is Spacelike in Rk+21
Nonnull Ruled Hypersurface Rk+21
2010/3/1
In this paper, the pitch and the angle of pitch of a closed nonnull ruled hypersurface whose generators are spacelike are calculated in Rk+21 .
The Hessian Tensor on a Hypersurface in Euclidean Space and Otsuki's Lemma
Hypersurface Euclidean Space Otsuki's Lemma
2010/3/5
The purpose of this paper is to obtain a condition for a hypersurface in Euclidean space with belongs to Hessian Tensor and is to give an alternative proof of Otsuki's lemma by applying this condition...