## 179 Citations

### Rational points on the intersection of three quadrics

- Mathematics
- 2017

We prove the Hasse principle and weak approximation for varieties defined by the smooth complete intersection of three quadratics in at least 19 variables, over arbitrary number fields.

### Rationality of complete intersections of two quadrics

- Mathematics
- 2019

We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a…

### Quadratic points on intersections of two quadrics

- Mathematics
- 2021

. We prove that a smooth complete intersection of two quadrics of dimension at least 2 over a number ﬁeld has index dividing 2, i.e., that it possesses a rational 0-cycle of degree 2.

### Pairs of quadrics in 11 variables

- MathematicsCompositio Mathematica
- 2015

For non-singular intersections of pairs of quadrics in 11 or more variables, we prove an asymptotic for the number of rational points in an expanding box.

### On intersections of two real quadrics

- Mathematics
- 2018

This paper is devoted to describing properties of complete intersections of two real projective quadrics. For brevity we call such varieties biquadrics. One of the main sections is devoted to real…

### Rationality of complete intersections of two quadrics over nonclosed fields

- MathematicsL’Enseignement Mathématique
- 2021

We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a…

### Algebraic Cycles and Intersections of 2 Quadrics

- Mathematics
- 2021

A smooth intersection Y of two quadrics in P has Hodge level 1. We show that such varieties Y have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain…

### Floer cohomology and pencils of quadrics

- Mathematics
- 2010

There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a…

### Ulrich Bundles on Intersections of Two 4-Dimensional Quadrics

- MathematicsInternational Mathematics Research Notices
- 2019

In this paper, we investigate the moduli space of Ulrich bundles on a smooth complete intersection of two $4$-dimensional quadrics in $\mathbb P^5$. The main ingredient is the semiorthogonal…

### Properties of legendrian subvarieties of projective space

- Mathematics
- 2005

I prove that every smooth legendrian variety generated by quadrics is a homogeneous variety and further I give a list of all such legendrian varieties. A review of the subject is included,…

## References

SHOWING 1-10 OF 12 REFERENCES

### Absolute gradient bound for surfaces of constant mean curvature

- Mathematics
- 1967

© Scuola Normale Superiore, Pisa, 1994, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze »…

### The Theory and Applications of Harmonic Integrals

- Mathematics
- 1941

1. Reimannian Manifolds 2. Integrals and their periods 3. Harmonic Integrals 4. Applications to algebraic varieties 5. Applications to the theory of continuous groups.

### The intermediate Jacobian of the cubic threefold

- Mathematics
- 1972

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and…

### Methods of algebraic geometry

- Mathematics
- 1947

“THIS volume is the first part of a work designed it provide a convenient account of the foundations and methods of modem algebraic geometry.” These words from the authors' preface explain the scope…

### Topological methods in algebraic geometry

- Mathematics
- 1966

Introduction Chapter 1: Preparatory material 1. Multiplicative sequences 2. Sheaves 3. Fibre bundles 4. Characteristic classes Chapter 2: The cobordism ring 5. Pontrjagin numbers 6. The ring…