Year: 2026
Type: preprint
Abstract: The main goal of this note is to relate two different Welschinger-type rules of signs that were used for definition of real enumerative invariants of toric surfaces (the invariants considered being relative to the toric boundary). The relation between them intertwines Mikhalkin's quantum index and geometry of real and complex point sets of counted real curves. As a by-product, we suggest a new definition of quantum index, which can be used for refined invariant enumeration of real algebraic curves on surfaces in a non-toric setup.
Source: arXiv (Cornell University)
Authors: Itenberg, Ilia, Shustin, Eugenii
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170301616
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