Counting curves on rational surfaces

By Ravi Vakil. 2000

101 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c093b3a46df77b7d55a38c96738d1841f3f8ac10

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Enumerative tropical algebraic geometry (2003, background): “This geometry allows to replace complex toric varieties with the real space Rn and holomorphic curves with certain piecewise-linear graphs there.”
Welschinger invariants of real Del Pezzo surfaces of degree ≥ 3 (2011, methodology): “We derive new real Caporaso-Harris type formulas (see Theorems 2 and 3) and real analogues of Abramovich-Bertram-Vakil formula [1, 22] (see Theorems 4 and 5).”
Counting curves via lattice paths in polygons (2002, unknown): “See 7] for”
Floor decompositions of tropical curves : the planar case (2008, methodology): “As an example we briefly outline here how to reconstruct Vakil’s formula [Vak00], which relates some enumerative invariants of Hirzebruch surfaces.”
Labeled floor diagrams for plane curves (2009, methodology): “Several approaches have been suggested to the computation of the Gromov–Witten numbers Nd,g , most notably the Caporaso–Harris recursive algorithm [10]; see also [15, 19, 22, 41, 42].”
A Caporaso-Harris type formula for Welschinger invariants of real toric Del Pezzo surfaces (2006, methodology): “Using the same arguments as in [9], Section 6.”
Floor diagrams relative to a conic, and GW-W invariants of Del Pezzo surfaces (2014, methodology): “These numbers have been first computed by Vakil [Vak00a].”
Enumerative tropical algebraic geometry in R^2 (2003, background): “This geometry allows one to replace complex toric varieties with the real space Rn and holomorphic curves with certain piecewise-linear graphs there.”
On Severi Varieties on Hirzebruch Surfaces (2006, background): “Most of the statements, ideas, and proofs presented here can be found in different sources (see for example [1,2,5,10], and [11] for related topics).”
Refined curve counting with tropical geometry (2014, background): “In [12] it is noted in case S = P(2), and in [26] for rational ruled surfaces, that the N (S,L),δ 0 can be expressed by a formula in terms of the Severi degrees N .”
Refined curve counting on complex surfaces (2012, methodology): “dC2 2 / ı 1 dC2 2 ı 1 ! qn : The generalization of this to n 0 is in [71].”