Milnor Number Equals Tjurina Number for Functions on Space Curves

MILNOR NUMBER EQUALS TJURINA NUMBER FOR FUNCTIONS ON SPACE CURVES Year of publication: 2001 Link to published version: http://dx.doi.org/10.1112/S0024610700001320 Publisher statement: None MILNOR NUMBER EQUALS TJURINA NUMBER FOR FUNCTIONS ON SPACE CURVES

Generating Functions for the Number of Curves on Abelian Surfaces

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves that pass through g generic points and we also count the number of curves in the fixed linear system |C| passing through g − 2 generic points. These two numbers, (defined appropriately) only depend ...

Milnor Number of Weighted-Lê–Yomdin Singularities

The Affine Stratification Number and the Moduli Space of Curves

We define the affine stratification number asnX of a scheme X . For X equidimensional, it is the minimal number asnX such that there is a stratification ofX by locally closed affine subschemes of codimension at most asnX . We show that the affine stratification number is well-behaved, and bounds many aspects of the topological complexity of the scheme, such as vanishing of cohomology groups of ...

The list distinguishing number equals the distinguishing number for interval graphs

A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from {1, . . . , k}. A list assignment to G is an assignment L = {L(v)}v∈V (G) of lists of colors to the...