On Manin's conjecture for singular del Pezzo surfaces of degree four, II

By R. Bretèche, Tim D Browning. Mathematical Proceedings of the Cambridge Philosophical Society, 2004

49 citations recorded by the source corpus.

Abstract This paper establishes the Manin conjecture for a certain non-split singular del Pezzo surface of degree four $X \subset \bfP^4$. In fact, if U ⊂ X is the open subset formed by deleting the lines from X, and H is the usual projective height function on $\bfP^4(\Q)$, then the height zeta function $ \sum_{x \in U(\Q)}{H(x)^{-s}} $ is analytically continued to the half-plane ℜe(s) > 17/20.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/efd74bb9f2311a700f2b0448d6c2c8b1c0be2ff9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ulrich Derenthal
2. Tim D Browning
3. Manjul Bhargava
4. Jürgen Hausen
5. Hendrik Suss

In Geometry and Topology

1. Ulrich Derenthal
2. Tim D Browning
3. Manjul Bhargava
4. Jürgen Hausen
5. Hendrik Suss

In Mathematical Physics

1. Ulrich Derenthal
2. Tim D Browning

Citations in the corpus

• Singular del Pezzo surfaces whose universal torsors are hypersurfaces (2006, background): “Type xiii, which was considered in more detail in [DT06] (see [BB05] for a non-split form), has the following properties: • It is given by the the following quadrics in P4: x0x3 − x1x4 = x0x1 + x1x3 + x 2 2 = 0.”
• An overview of Manin's conjecture for del Pezzo surfaces (2005, background): “This equation gives an affine embedding of the unique universal torsor over S̃3, though we shall not prove it here.”