32 citations · 48 across the 6 of their papers we have counts for
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Equisingular Families of Projective Curves
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular,…
Appendix to "Welschinger invariant and enumeration of real rational curves"
Ilia Itenberg, Viatcheslav Kharlamov, Eugenii Shustin
The invariance of the Welschinger numbers for real unnodal Del Pezzo surfaces, which we used for the enumeration of real rational curves on real toric Del Pezzo surfaces (see math.…
Welschinger invariant and enumeration of real plane rational curves
I. Itenberg, V. Kharlamov, E. Shustin
Welschinger's invariant bounds from below the number of real rational curves through a given generic collection of real points in the real projective plane. We estimate this invari…
Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry
Eugenii Shustin
We prove a new patchworking theorem for singular algebraic curves, which states the following. Given a complex toric threefold which fibers over with a reduced re…
Analytic order of singular and critical points
Eugenii Shustin
We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analyt…
Castelnuovo function, zero-dimensional schemes and singular plane curves
Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin
We study families V of curves in P^2 of degree d having exactly r singular points of given topological or analytic types. We derive new sufficient conditions for V to be T-smooth (…