140 research outputs found
Polar Cremona Transformations and Monodromy of Polynomials
Consider the gradient map associated to any non-constant homogeneous
polynomial f\in \C[x_0,...,x_n] of degree , defined by \phi_f=grad(f):
D(f)\to \CP^n, (x_0:...:x_n)\to (f_0(x):...:f_n(x)) where D(f)=\{x\in \CP^n;
f(x)\neq 0\} is the principal open set associated to and
. This map corresponds to polar Cremona
transformations. In Proposition \ref{p1} we give a new lower bound for the
degree of under the assumption that the projective hypersurface
has only isolated singularities. When , Theorem \ref{t4}
yields very strong conditions on the singularities of .Comment: 8 page
Non-abelian resonance: product and coproduct formulas
We investigate the resonance varieties attached to a commutative differential
graded algebra and to a representation of a Lie algebra, with emphasis on how
these varieties behave under finite products and coproducts.Comment: 12 page
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