59 citations · 309 across the 51 of their papers we have counts for
56 papers
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…
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…
Refined tropical invariants and characteristic numbers
Eugenii Shustin, Uriel Sinichkin
We prove that the Göttsche-Schroeter and Schroeter-Shustin refined invariants specialize at to the enumeration of rational, resp. elliptic complex curves on arbitrary toric s…
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…
Real enumerative invariants relative to the anti-canonical divisor and their refinement
Ilia Itenberg, Eugenii Shustin
We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real elliptic curves. These inva…
Tropical vertex and real enumerative geometry
Eugenii Shustin
We show that the commutator relations in the refined tropical vertex group can be expressed via the enumeration of suitable real rational curves in toric surfaces.