MathOverflow

Let $X$ be a smooth algebraic surface and let $L$ be a very ample divisor on it.
Question. Under which conditions on the pair $(X, \, L)$ can we find a curve $C \in |6L|$ having $6L^2$ ordinary cusps in general positions and no othersingularities?
Motivation. When $X=\mathbb{P}^2$ and $L=\mathcal{O}(1)$, I am looking for curves of degree $6$ with six ordinary cusps in general position. Now, taking a curve of type $$f(x_0, \, x_1, \, x_2)^2=g(x_0, \, x_1, \, x_2)^3,$$where $\deg f=3, \, \deg g...

I am reading Kunen's books on set theory and logic. In his approach, the metatheory is finitistic (which can be approximated in PRA).
This implies that in the finitistic metatheory, one can do formal logic, and come up with finite languages $\mathcal{L}$, describe finite formulas and finite proofs....

I'm interested in finding the (unique?) solution to the set of delay differential equations$$f_w(w,x) = xf(w,w^2x)+w^3x^2f(w,w^4x), $$$$f_x(w,x) = wf(w,w^2x)$$With the initial condition $f(1,x) = e^x$ and $(w,x) \in \mathbb{C}^2$
For $|w| \leq 1$, I've found the series $f(w,x) = \sum_{n=0}^\infty \frac{w^{n^2} x^n}{n!}$ satisfies the equations, but it doesn't converge for $|w|>1$....

In algebraic geometry, flat morphisms are usually associated with the intuition that they have „continuously varying fibers”. Is there a notion in topology formalizing the same intuition? Consider for example a map $p \colon P \to X$ of good (locally...