59 citations · 253 across the 29 of their papers we have counts for
32 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…
Real plane sextics without real points
Alex Degtyarev, Ilia Itenberg
We prove that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, \ie, the polarization, excepti…
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…
Planes in cubic fourfolds
Alex Degtyarev, Ilia Itenberg, John Christian Ottem
We show that the maximal number of planes in a complex smooth cubic fourfold in is , realized by the Fermat cubic only; the maximal number of real planes in a…
Area in real K3-surfaces
Ilia Itenberg, Grigory Mikhalkin
For a real K3-surface , one can introduce areas of connected components of the real point set of using a holomorphic symplectic form of . These areas are d…