2006/05/27 by Eugeniĭ Shustin, Shustin, E.
Computer Science · Mathematics · #14H20 #14M25 #14N10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 14H15. Secondary 12J25
paper · pdf · doi:10.48550/arxiv.math/0605697
openalex publication_date 2006/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Welschinger invariants of real rational algebraic surfaces are natural analogues of the Gromov-Witten invariants, and they estimate from below the number of real rational curves passing through prescribed configurations of points. We establish a tropical formula for the Welschinger invariants of four toric Del Pezzo surfaces, equipped with a non-standard real structure. Such a formula for real toric Del Pezzo surfaces with a standard real structure (i.e., naturally compatible with the toric structure) was established by Mikhalkin and the author. As a consequence we prove that, for any real ample divisor D on a surfaces Σ under consideration, through any generic configuration of c1(Σ)D-1 generic real points there passes a real rational curve belonging to the linear system |D|.