Degeneracy Loci and Polynomial Equation Solving

Degeneracy loci and polynomial equation solving

Let V be a smooth equidimensional quasi-affine variety of dimension r over C and let F be a (p× s)-matrix of coordinate functions of C[V ], where s ≥ p+ r. The pair (V, F ) determines a vector bundle E of rank s− p over W := {x ∈ V | rkF (x) = p}. We associate with (V, F ) a descending chain of degeneracy loci of E (the generic polar varieties of V represent a typical example of this situation)...

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Degeneracy loci and polynomial equation solving 1 Bernd Bank

Let V be a smooth equidimensional quasi-affine variety of dimension r over C and let F be a (p× s)-matrix of coordinate functions of C[V ], where s ≥ p+ r. The pair (V, F ) determines a vector bundle E of rank s− p over W := {x ∈ V | rkF (x) = p}. We associate with (V, F ) a descending chain of degeneracy loci of E (the generic polar varieties of V represent a typical example of this situation)...

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D ec 2 01 3 Degeneracy loci and polynomial equation solving 1

Let V be a smooth equidimensional quasi-affine variety of dimension r over C and let F be a (p× s)-matrix of coordinate functions of C[V ], where s ≥ p+ r. The pair (V, F ) determines a vector bundle E of rank s− p over W := {x ∈ V | rkF (x) = p}. We associate with (V, F ) a descending chain of degeneracy loci of E (the generic polar varieties of V represent a typical example of this situation)...

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ec 2 01 3 Degeneracy loci and polynomial equation solving 1

Let V be a smooth equidimensional quasi-affine variety of dimension r over C and let F be a (p× s)-matrix of coordinate functions of C[V ], where s ≥ p+ r. The pair (V, F ) determines a vector bundle E of rank s− p over W := {x ∈ V | rkF (x) = p}. We associate with (V, F ) a descending chain of degeneracy loci of E (the generic polar varieties of V represent a typical example of this situation)...

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Solving Polynomial Systems Equation by Equation∗

By a numerical continuation method called a diagonal homotopy, one can compute the intersection of two irreducible positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure to intersect general solution sets that are not necessarily irreducible or even equidimensional. Of particular interest is the special case whe...

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Degeneracy Loci and Polynomial Equation Solving

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