## View abstract

### Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Tuesday, July 20, 18:50 ~ 19:40 UTC-3

## On the lower bound for the degree of a hypothetical counterexample to the plane Jacobian conjecture

### Christian Valqui

#### Pontifical Catholic University of Peru, Peru   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloaka4059dec84fccb796819bac85ecbe2f5').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addya4059dec84fccb796819bac85ecbe2f5 = 'cv&#97;lq&#117;&#105;' + '&#64;'; addya4059dec84fccb796819bac85ecbe2f5 = addya4059dec84fccb796819bac85ecbe2f5 + 'p&#117;cp' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'p&#101;'; var addy_texta4059dec84fccb796819bac85ecbe2f5 = 'cv&#97;lq&#117;&#105;' + '&#64;' + 'p&#117;cp' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'p&#101;';document.getElementById('cloaka4059dec84fccb796819bac85ecbe2f5').innerHTML += '<a ' + path + '\'' + prefix + ':' + addya4059dec84fccb796819bac85ecbe2f5 + '\'>'+addy_texta4059dec84fccb796819bac85ecbe2f5+'<\/a>';

We use the detailed description of the shape of the support of a hypothetical minimal counterexample $(P,Q)$ to the plane Jacobian conjecture in order to discard all cases of $(\deg(P),\deg(Q))$ satisfying $\max\{\deg(P),\deg(Q)\}< 125$, except the pair $(72,108)$ (and the symmetric pair $(108,72)$), thus increasing the lower bound of $100$ obtained by Moh up to $108$.

This is a joint work with Rodrigo Horruitiner, Juan José Guccione and Jorge Guccione.