Differentiability of volumes of divisors and a problem of Teissier
By S. Boucksom, C. Favre, Mattias Jonsson. 2006
185 citations recorded by the source corpus.
We give an algebraic construction of the positive intersection products of pseudo-effective classes and use them to prove that the volume function on the Neron-Severi space of a projective variety ...
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/7123e8bcffbd195e6695b3196a586954d13f8bf3
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
- Chi Li
- M. Mustaţă
- Brian Lehmann
- Robert J. Berman
- S. Boucksom
- Steven Dale Cutkosky
- R. Lazarsfeld
- Vincent Guedj
In Computational Theory and Mathematics
- Chi Li
- M. Mustaţă
- Brian Lehmann
- Robert J. Berman
- S. Boucksom
- Steven Dale Cutkosky
- R. Lazarsfeld
- Philippe Eyssidieux
In Geometry and Topology
- Chi Li
- Robert J. Berman
- S. Boucksom
- Mattias Jonsson
- Yuchen Liu
- Vincent Guedj
- Tam'as Darvas
- Ahmed Zeriahi
Citations in the corpus
- Convex Bodies Associated to Linear Series (2008, methodology): “Corollary C was one of the starting points of the interesting work [9] of Boucksom–Favre–Jonsson, who found a nice formula for the derivative of volX in any direction, and used it to answer some questions of Teissier.”
- Geodesic rays and stability in the cscK problem (2020, background): “It is well known that the above argument amounts to the algebraic fact that toric divisors on toric varieties always admit a rational Zariski decomposition (see [13]).”
- Comparing numerical dimensions (2011, methodology): “The statement is proved in [Boucksom et al. 2009] only when the L i are V -big, but the proposition extends to the V -pseudoeffective case by taking limits.”
- Growth of balls of holomorphic sections and energy at equilibrium (2008, background): “It bears a strong resemblance with the differentiability property of the volume of divisors [27], which is in some sense a non-archimedean analogue of the present result (compare [26]).”
- Asymptotic Multiplicities of Graded Families of Ideals and Linear Series (2014, background): “Interpretation of the directional derivative in terms of intersection products and many applications are given in [2], [14], [28] and [7].”