## View abstract

### Session II.6 - Computational Algebraic Geometry

Friday, June 16, 17:00 ~ 17:30

## Subresultants and the Shape Lemma

### Carlos D'Andrea

#### Universitat de Barcelona, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloake834d1dc64416c1a83eaab4738d4cfe5').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addye834d1dc64416c1a83eaab4738d4cfe5 = 'cd&#97;ndr&#101;&#97;' + '&#64;'; addye834d1dc64416c1a83eaab4738d4cfe5 = addye834d1dc64416c1a83eaab4738d4cfe5 + '&#117;b' + '&#46;' + '&#101;d&#117;'; var addy_texte834d1dc64416c1a83eaab4738d4cfe5 = 'cd&#97;ndr&#101;&#97;' + '&#64;' + '&#117;b' + '&#46;' + '&#101;d&#117;';document.getElementById('cloake834d1dc64416c1a83eaab4738d4cfe5').innerHTML += '<a ' + path + '\'' + prefix + ':' + addye834d1dc64416c1a83eaab4738d4cfe5 + '\'>'+addy_texte834d1dc64416c1a83eaab4738d4cfe5+'<\/a>';

In nice cases, a zero-dimensional complete intersection ideal over a field has a Shape Lemma. There are also cases where the ideal is generated by the resultant and first subresultant polynomials of the generators. This situation has been explored by Agnes Szanto in some earlier papers in her academic career. We will review them and explore the relation between these representations, and also study when the resultant generates the elimination ideal.

Joint work with David Cox (Amherst College, USA).