## View abstract

### Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 14, 13:30 ~ 14:00 UTC-3

## Bounds for degrees of syzygies

### Carlos D'Andrea

#### Universitat de Barcelona, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak71538feb9ffb79c6eb32080ea7031264').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy71538feb9ffb79c6eb32080ea7031264 = 'cd&#97;ndr&#101;&#97;' + '&#64;'; addy71538feb9ffb79c6eb32080ea7031264 = addy71538feb9ffb79c6eb32080ea7031264 + '&#117;b' + '&#46;' + '&#101;d&#117;'; var addy_text71538feb9ffb79c6eb32080ea7031264 = 'cd&#97;ndr&#101;&#97;' + '&#64;' + '&#117;b' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak71538feb9ffb79c6eb32080ea7031264').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy71538feb9ffb79c6eb32080ea7031264 + '\'>'+addy_text71538feb9ffb79c6eb32080ea7031264+'<\/a>';

We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of $m$ polynomials in $n$ variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results.

Joint work with Teresa Cortadellas Benitez (Universitat de Barcelona) and Eulalia Montoro (Universitat de Barcelona).