منابع مشابه
Kodaira Dimension of Moduli of Special Cubic Fourfolds
A special cubic fourfold is a smooth hypersurface of degree three and dimension four that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether-Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties....
متن کاملModular Curves, Modular Surfaces, and Modular Fourfolds
We begin with some general remarks. Let X be a smooth projective variety of dimension n over a field k. For any positive integer p < n, it is of interest to understand, modulo a natural equivalence, the algebraic cycles Y = ∑ j mjYj lying on X, with each Yj closed and irreducible of codimension p, together with codimension p + 1 algebraic cycles Zj = ∑ i rijZij lying on Yj , for all j. There is...
متن کاملTwisted Cubics on Cubic Fourfolds
We construct a new twenty-dimensional family of projective eight-dimensional holomorphically symplectic manifolds: the compactified moduli space M3(Y ) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M3(Y ) → Z(Y ) to a projective eight-dimensional symplectic manifold Z(Y ). The construction is based on results on lin...
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We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.
متن کاملCubic Fourfolds and Spaces of Rational Curves
For a general nonsingular cubic fourfold X ⊂ P5 and e ≥ 5 an odd integer, we show that the space Me parametrizing rational curves of degree e on X is non-uniruled. For e ≥ 6 an even integer, we prove that the generic fiber dimension of the maximally rationally connected fibration of Me is at most one, i.e. passing through a very general point of Me there is at most one rational curve. For e < 5...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2013.06.003