1 Exhibit 23.1 CONSENT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS We consent to the incorporation by reference in the Registration Statements (Form S-3 Nos. 333-70355 and 333-51013 and Form S-8 Nos. 333-12487, 333-33635, 333-33637, 333-71181) and the related prospectuses of Geron Corporation of our report dated February 12, 1999, with respect to the financial statements of Geron Corporation included in the Annual Report (Form 10-K) for the year ended December 31, 1998. /s/ ERNST & YOUNG LLP --------------------------------- Palo Alto, California March 12, 1999