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Tangency and Discriminants
Published on Jul 19, 2019140 Views
The discriminant of a polynomial with prescribed monomials is an irreducible polynomial in the coefficients vanishing when the corresponding polynomial has multiple roots. It is an important tool in n
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Chapter list
Tangency and Discriminants00:00
Goal00:54
Natural concept02:27
The discriminants of univariate polynomials04:13
Algebra vs Geometry06:12
The definition of discriminant - 109:52
The definition of discriminant - 212:03
Example 114:31
Geometry - 115:42
Geometry - 219:47
Projective duality - 120:58
Projective duality - 223:54
Polar geometry:the degree and dimension of the discriminant27:07
Toric projective duality = A-discriminants30:00
Can a discriminant govern multiple roots of systems of polynomials?35:12
Example - 137:11
Tangential intersections37:45
The mixed discriminant39:09
Example - 240:36
One more example: The distance to a variety41:59
Consider now a plane curve43:12
This proves:44:34
Singular intersection of Quadric Surfaces46:53
Two Main Questions47:38
Towards an answer to question 148:24
Answer to question 152:36
Answer to question 254:31
Thank you55:26