3 papers
math.AG2026
Quantum index, Arnold-Rokhlin surfaces, and real enumerative geometry
Ilia Itenberg, Eugenii Shustin
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…
math.AG2026
Anti-Zariski pairs
Peng Ren, Eugenii Shustin
In 1929, O. Zariski found a pair of complex plane algebraic curves of the same degree and with the same collection of singularities, but embedded into the plane in a topologically…
math.AG2025
Real enumerative invariants relative to the toric boundary and their refinement
Ilia Itenberg, Eugenii Shustin
We introduce new invariants of a class of toric surfaces (including the projective plane) that arise from appropriate enumeration of real curves of genus one and two. These invaria…