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7 votes
3 answers
969 views

Basepoints in the canonical system of algebraic surfaces

Let $X$ be a smooth projective variety defined over $\mathbb{C}$. In the context of the minimal model program it is often important to understand the geometry of the maps defined by the complete ...
Clay Cordova's user avatar
  • 2,087
7 votes
1 answer
490 views

General conditions for normality of blow-up

Let $X$ be an integral, affine, normal complex surface. I am looking for conditions on zero-dimensional closed subschemes $Z$ in $X$ such that the reduced scheme associated to the blow-up of $X$ along ...
Jana's user avatar
  • 2,022
3 votes
1 answer
242 views

Linear homogenous polynomials that generates several quadratic polynomials

This is a generalization of this question. Let $P_1, \ldots, P_m$, $Q_1, \ldots, Q_k \in \mathbb{C}[x_0,\ldots,x_n]$ be linear homogenous polynomials. Let $f_1, \ldots, f_s$ be a homogenous ...
Alexey Milovanov's user avatar
2 votes
3 answers
341 views

Linear homogenous polynomials that generates one quadratic polynomial

Let $P_1, \ldots, P_m$, $Q_1, \ldots, Q_k \in \mathbb{C}[x_0,\ldots,x_n]$ be linear homogenous polynomials. Let $f$ be a homogenous quadratic polynomial of degree $2$. Assume that for every $i$ and ...
Alexey Milovanov's user avatar