منابع مشابه
Eckardt Loci on Hypersurfaces
We compute the dimensions and cohomology classes of the loci on a general hypersurface where the second fundamental form has rank at most r. We also determine the number of hypersurfaces in a general pencil in Pn, with n = `q+1 2 ́ , that contain a point where the second fundamental form has rank n− 1− q. These results generalize many classical formulae.
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All varieties are assumed to be projective and defined over a field of characteristic 0, unless mentioned. Main definitions and notations appear in [KMM] and [Sh93]. Classically, an Eckardt point is a point on a nonsingular cubic surface Σ at which three lines on this surface intersect each other. In other words, it is a point p on Σ such that there is an element in | − KΣ| which is a cone with...
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A symplectic variety is a normal complex variety X with a holomorphic symplectic form ω on the regular part X reg and with rational Gorenstein sin-gularities. Affine symplectic varieties arise in many different ways such as closures of nilpotent orbits of a complex simple Lie algebra, as Slodowy slices to such nilpotent orbits or as symplectic reductions of holomorphic symplec-tic manifolds wit...
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Let X be a smooth hypersurface of degree n ≥ 3 in P. We prove that the log canonical threshold of H ∈ |−KX| is at least n−1 n . Under the assumption of the Log minimal model program, we also prove that a hyperplane section H of X is a cone in P over a smooth hypersurface of degree n in P if and only if the log canonical threshold of H is n−1 n . Bibliography : 20 titles.
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Let g ∈ Z[x1, . . . , xn] be an absolutely irreducible cubic polynomial whose homogeneous part is non-degenerate. The primary goal of this paper is to investigate the set of integer solutions to the equation g = 0. Specifically, we shall try to determine conditions on g under which we can show that there are infinitely many solutions. An obvious necessary condition for the existence of integer ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2015
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2014.910798