A primer on Seshadri constants

By Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Michał Kapustka, A. Knutsen, W. Syzdek, Tomasz Szemberg. 2008

150 citations recorded by the source corpus.

Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced by Demailly. The original idea of using them towards a proof of the Fujita conjecture failed but they quickly became a subject of intensive study quite in their own right. Lazarsfeld's book "Positivity in Algebraic Geometry" contains a whole chapter devoted to local positivity and serves as a very enjoyable introduction to Seshadri constants. Since this book has appeared, the subject witnessed quite a bit of development. It is the aim of these notes to give an account of recent progress as well as to discuss many open questions and provide some examples.

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

View Paper: https://www.semanticscholar.org/paper/53441fbe183e23ee97b3962be771764099deb830

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In Algebra and Number Theory

1. Juan Migliore
2. Brian Harbourne
3. A. V. Geramita
4. Craig Huneke
5. F. Catanese
6. Ingrid Bauer
7. Chi Li
8. Uwe Nagel

In Geometry and Topology

1. Ingrid Bauer
2. Juan Migliore
3. Brian Harbourne
4. A. V. Geramita
5. F. Catanese
6. Craig Huneke
7. Chi Li
8. Y. Odaka

In Mathematical Physics

1. Ingrid Bauer
2. F. Catanese
3. Chi Li
4. Brian Harbourne
5. Craig Huneke
6. Matteo Penegini
7. Fritz Grunewald
8. G. González‐diez

Citations in the corpus

• Global aspects of the geometry of surfaces (2009, unknown): “See [PSC] for greater generality.”
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• ARE SYMBOLIC POWERS HIGHLY EVOLVED (2011, result): “r the maximum height of the associated primes. If e is the maximum of the heights of the associated primes of a given homogeneous ideal I, then from [HH1] we know I(re) ⊆ Ir, and it is conjectured in [PSC] that I(re−(e−1)) ⊆ Ir. This raises the question of whether I(re) ⊆ Mr(e−1)Ir and I(re−(e−1)) ⊆”
• Star configurations in Pn (2013, background): “These have arisen as objects of study in numerous research projects lately, including [2, 3, 5, 6, 8, 13, 21, 26], but these references make use of only a partial understanding of the properties of star configurations.”
• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, methodology): “4–fold blow up and it acquires two more pairs of infinitely near (−1)–curves. EMPTINESS OF HOMOGENEOUS LINEAR SYSTEMS WITH TEN GENERAL BASE POINTS 3 (2) Six disjoint curves, i.e. two conics C1 = L2(14,[1,0],[0,0]), C2 = L2(14,[0,0],[1,0]) and four quartics Qj = L4(23,1,[1,1]2) on V1 (the multiplicity”
• Minimizing normalized volumes of valuations (2015, background): “2 pointed out to me by an anonymous referee. This proof is more in the spiritual of [Izu85] and is based on the argument of Boucksom-Favre-Jonsson in [BFJ12, Section 3.1] and the following Fact: (see [Betal09]) For any smooth projective variety X′ and any ample line bundle L → X ′, there exists a po”