Narrow Results

We describe open book decompositions of links of simple surface singularities that support the corresponding unique Milnor fillable contact structures. The open books we describe are isotopic to Milnor open books.

We derive a Bouchard–Eynard type topological recursion for the total descendant potential of $A_N$-singularity. Our argument relies on a certain twisted representation of a Heisenberg Vertex Operator Algebra (VOA) constructed via the periods of $A_N$-singularity. In particular, our approach allows us to prove that the topological recursion for the total descendant potential is equivalent to a certain generating set of ${𝒲}$-algebra constraints.

Very few examples of obstructed equsingular families of curves on surfaces other than ℙ² are known. Combining results from [1] and [2] with an idea from [3] we give in the present paper series of examples of families of irreducible curves with simple singularities on surfaces in ℙ³ which are not T-smooth, i.e. do not have the expected dimension, (Sec. 2) and we compare this with conditions (showing the same asymptotics) which ensure the existence of a T-smooth component (Sec. 3).