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In the following context: Let $S$ be a connected smooth projective surface over $\mathbb{C}$, and let $\Sigma$ be the complete linear system of a very ample divisor $D$ on $S$. Let $d=\dim(\Sigma)$ ...

Let $M_m := (f_1, \cdots, f_m )$ be an algebraic map from $\mathbb{R}^n$ to $\mathbb{R}^m$ and $f_1^2,...,f_m^2$ are homogeneous polynomials of the same degree in $Q[x_1,...,x_n]$ . Similarly define $...

I am aware that this is not a esearch question, but I don't know where else to ask. I have come across the fact that the stack of bundles of rank r and degree d over a curve of genus g with a ...

The Wikipedia entry on intersection theory contains the following statement: [for C a curve, on a surface] "the self-intersection points of C is the generic point of C, taken with multiplicity C · C."...

Let $V$ be a smooth manifold, $E \rightarrow V$ a vector bundle over $V$ and $\Gamma$ be a finite group acting nontrivially on $V$ and $E$. Let $s \in C^\infty(E)$ be a generic $\Gamma$-equivariant ...

In algebraic geometry, an irreducible scheme has a point called "the generic point." The justification for this terminology is that under reasonable finiteness hypotheses, a property that is true at ...