Skip to main content
MathOverflow

Return to Question

added 2 characters in body
Source Link
DCT
DCT
  • 1.5k
  • 9
  • 15

Let $W_d$ be the vector space of degree $d$ homogenous polynomials in $n+1$ variables. If we fix $d_1,\ldots,d_m$, we can consider the locus $Z\subset \mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$ parameterizing $m$-tuples of hyperplaneshypersurfaces that fail to be a complete intersection. Do we know anything about the codimension of $Z$ in $\mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$?

Let $W_d$ be the vector space of degree $d$ homogenous polynomials in $n+1$ variables. If we fix $d_1,\ldots,d_m$, we can consider the locus $Z\subset \mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$ parameterizing $m$-tuples of hyperplanes that fail to be a complete intersection. Do we know anything about the codimension of $Z$ in $\mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$?

Let $W_d$ be the vector space of degree $d$ homogenous polynomials in $n+1$ variables. If we fix $d_1,\ldots,d_m$, we can consider the locus $Z\subset \mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$ parameterizing $m$-tuples of hypersurfaces that fail to be a complete intersection. Do we know anything about the codimension of $Z$ in $\mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$?

Source Link
DCT
DCT
  • 1.5k
  • 9
  • 15

Collection of hypersurfaces failing to be a complete intersection

Let $W_d$ be the vector space of degree $d$ homogenous polynomials in $n+1$ variables. If we fix $d_1,\ldots,d_m$, we can consider the locus $Z\subset \mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$ parameterizing $m$-tuples of hyperplanes that fail to be a complete intersection. Do we know anything about the codimension of $Z$ in $\mathbb{P}W_{d_1}\times\cdots\mathbb{P}W_{d_m}$?