Let $X$ be a $n$-dimensional complex projective algebraic variety, let us suppose that $X$ has only isolated singularities.

Edit: Let us say that an ordinary $m$-ple singular point is an isolated singular point such that the tangent cone to this point is the cone over a $n-1$-dimensional smooth hypersurface $H\subset \mathbb{C}P^n$ of degree $m$.

If $X$ has only such ordinary $m$-ple points what do we know about the geometry and topology of $X$?:

1. What about the Mixed Hodge structure on the singular cohomology of $X$?

2. What about the topology of resolutions of $X$?

3. When do small resolutions exist?

4. Do there exist some relations between the number of ordinary multiple points, their multiplicities and some geometric or topological invariants of $X$?

What are the classical references for such algebraic varieties?

Let $X$ be a $n$-dimensional complex projective algebraic variety, let us suppose that $X$ has only isolated singularities.

Edit: Let us say that an ordinary $m$-ple singular point is an isolated singular point such that the tangent cone to this point is the cone over a $n-1$-dimensional smooth hypersurface $H\subset \mathbb{C}P^n$ of degree $m$.

If $X$ has only such ordinary $m$-ple points what do we know about the geometry and topology of $X$ and of its resolutions?:

1. What about the Mixed Hodge structure on the singular cohomology of $X$ and of its resolutions?

2. When do small resolutions exist ($IH$-small)? If $X$ is a threefold and has only nodes then small resolutions exist, what about other multiplicities and dimensions?

3. Do there exist some relations between the number of ordinary multiple points, their multiplicities and some geometric or topological invariants of $X$?

Let $X$ be a $n$-dimensional complex projective algebraic variety, let us suppose that $X$ has only isolated singularities.

What is exactly an ordinary $m$-tuple singular point? Am I correct if I say that the tangent cone to this point is the cone over a $n-1$-dimensional smooth hypersurface $H\subset \mathbb{C}P^n$? Then the multiplicity of the singular point is given by the degree of the hypersurface.

If $X$ has only such ordinary $m$-tuple points what do we know about the geometry and topology of $X$? For example what about the Mixed Hodge structure on the singular cohomology of $X$? What about the topology of resolutions of $X$? When do small resolutions exist? Do there exist some relations between the number of ordinary multiple points, their multiplicities and some geometric or topological invariants of $X$?

What are the classical references for such algebraic varieties?

Let $X$ be a $n$-dimensional complex projective algebraic variety, let us suppose that $X$ has only isolated singularities.

Edit: Let us say that an ordinary $m$-ple singular point is an isolated singular point such that the tangent cone to this point is the cone over a $n-1$-dimensional smooth hypersurface $H\subset \mathbb{C}P^n$ of degree $m$.

If $X$ has only such ordinary $m$-ple points what do we know about the geometry and topology of $X$?:

1. What about the Mixed Hodge structure on the singular cohomology of $X$?

2. What about the topology of resolutions of $X$?

3. When do small resolutions exist?

4. Do there exist some relations between the number of ordinary multiple points, their multiplicities and some geometric or topological invariants of $X$?

What are the classical references for such algebraic varieties?