Your Waterstones card is changing, introducing...
TELL ME MORE
Existence of the Sectional Capacity - Memoirs of the American Mathematical Society (Paperback)
  • Existence of the Sectional Capacity - Memoirs of the American Mathematical Society (Paperback)
zoom

Existence of the Sectional Capacity - Memoirs of the American Mathematical Society (Paperback)

£50.95
Paperback Published: 30/04/2000
  • Not available

This product is currently unavailable.

  • This item has been added to your basket
Let $K$ be a global field, and let $X/K$ be an equidimensional, geometrically reduced projective variety. For an ample line bundle $\overline{\mathcal L}$ on $X$ with norms $\\ \_v$ on the spaces of sections $K_v \otimes_K \Gamma(X,\L^{\otimes n})$, we prove the existence of the sectional capacity $S_Gamma(\overline{\mathcal L})$, giving content to a theory proposed by Chinburg. In the language of Arakelov Theory, the quantity $-\log(S_Gamma(\overline{\mathcal L}))$ generalizes the top arithmetic self-intersection number of a metrized line bundle, and the existence of the sectional capacity is equivalent to an arithmetic Hilbert-Samuel Theorem for line bundles with singular metrics.In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S_Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C_v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.

Publisher: American Mathematical Society
ISBN: 9780821820582
Weight: 283 g

You may also be interested in...

Introduction to Topology
Added to basket
Elliptic Tales
Added to basket
£13.99
Paperback
Euclid's Elements
Added to basket
£21.99
Paperback
Geometry
Added to basket
£44.99
Paperback
Introducing Fractals
Added to basket
Drawing Geometry
Added to basket
£12.99
Paperback
Maths for Science
Added to basket
£35.99
Paperback
Algebraic Topology
Added to basket
£30.99
Paperback
Ruler and Compass
Added to basket
£5.99
Paperback
Euclid's Window
Added to basket
Mathematical Origami
Added to basket

Reviews

Please sign in to write a review

Your review has been submitted successfully.