From Symplectic Packing to Algebraic Geometry and Back
By P. Biran. 2001
58 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb4f126b476b347193626264e61ae20069c5b1b2
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Gromov width of complex Grassmannians (2004, background): “Computations of Gromov width and, more generally, of symplectic ball packings, can be found, for example, in [4, 5, 6, 8, 16, 19].”
- Quantitative symplectic geometry (2005, unknown): “A strategy for studying symplectic embeddings of 4-dimensional ellipsoids by algebro-geometric tools is proposed in [6].”
- Quantitative embedded contact homology (2010, background): “ke ε → 0. Lemma 3.3 then extends to the possibly degenerate case: Proposition 3.6. Let (X,ω) be a weakly exact symplectic cobordism from (Y+,λ+) to (Y−,λ−). Assume that X is diffeomorphic to a product [0,1]×Y . Then for every positive integer k we have eck(Y−,λ−) ≤ eck(Y+,λ+). Proof. If f+ and f− are”
- Uniqueness of symplectic structures (2012, background): “An earlier theorem by Biran [5] asserts that Kcstd ⊂ Scstd ⊂ K cstd .”
- Symplectic embedding problems, old and new (2017, result): “We refer to [13] and [71, §5] for motivations coming from algebraic geometry, and in particular from an old conjecture of Nagata in enumerative algebraic geometry, which was in turn motivated by Hilbert’s fourteenth problem.”
- The embedding capacity of 4-dimensional symplectic ellipsoids (2009, background): “Moreover, its graph is linear on each subinterval [1, 2], [2, 4], [4, 5], [5, 6].”
- Quantum Structures for Lagrangian Submanifolds (2007, background): “Another important ingredient in the theory of absolute symplectic packing consists of criteria for realizing 2-dimensional cohomology classes by symplectic/Kähler forms such as the Nakai-Moishezon criterion (see [11, 13, 12] for symplectic analogues of this).”
- Lecture Notes on Embedded Contact Homology (2013, background): “ (a) ECH capacities give a sharp obstruction to symplectically embedding a disjoint union of balls of possibly different sizes into a ball. This follows by comparison with work of McDuff [41] and Biran [1] from the 1990’s which solved this embedding problem. See [26] for details. (b) It follows from w”