# Cubic fourfolds fibered in sextic del Pezzo surfaces

@article{Addington2019CubicFF, title={Cubic fourfolds fibered in sextic del Pezzo surfaces}, author={Nicolas Addington and Nicolas Brendan Yuri Anthony Hassett and Nicolas Brendan Yuri Anthony Tschinkel and Nicolas Brendan Yuri Anthony V{\'a}rilly-Alvarado}, journal={American Journal of Mathematics}, year={2019}, volume={141}, pages={1479 - 1500} }

Abstract:We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimen\-sion-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.

#### 24 Citations

Rational cubic fourfolds in Hassett divisors

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We prove that every Hassett's Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two subvarieties, parametrizing rational cubic fourfolds, in the moduli space… Expand

Fibrations in sextic del Pezzo surfaces with mild singularities

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We study sextic del Pezzo surface fibrations via root stacks. Mathematics Subject Classification (2020). Primary: 14D06; Secondary: 14F22, 14J26.

New rational cubic fourfolds arising from Cremona transformations

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Are Fourier--Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce… Expand

Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds

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Abstract In this article, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.

Representability of Chow groups of codimension three cycles

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Abstract Assume that we have a fibration of smooth projective varieties X → S over a surface S such that X is of dimension four and that the geometric generic fiber has finite-dimensional motive and… Expand

A remark on algebraic cycles on cubic fourfolds

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In this short note we try to generalize the Clemens-Griffiths criterion of non-rationality for smooth cubic threefolds to the case of smooth cubic fourfolds.

Refinement of the classification of weak Fano threefolds with sextic del Pezzo fibrations

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We refine the classification of weak Fano threefolds with sextic del Pezzo fibrations by considering the Hodge numbers of them. By the refined classification result, such threefolds are classified… Expand

Rational cubic fourfolds with associated singular K3 surfaces

- Mathematics
- 2020

Generalizing a recent construction of Yang and Yu, we study to what extent one can intersect Hassett's Noether-Lefschetz divisors $\mathcal{C}_d$ in the moduli space of cubic fourfolds $\mathcal{C}$.… Expand

On lattice polarizable cubic fourfolds

- Mathematics
- 2021

We extend non-emtpyness and irreducibility of Hassett divisors to the moduli spaces of M -polarizable cubic fourfolds for higher rank lattices M , which in turn provides a systematic approach for… Expand

Relative linear extensions of sextic del Pezzo fibrations over curves

- Mathematics
- 2018

We show that every sextic del Pezzo fibration over a curve (with a smooth total space and relative Picard rank one) is a relative linear section of a Mori fiber space with the general fiber… Expand

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