WASHINGTON, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT
                     Pursuant to Section 13 or 15(d) of the
                       SECURITIES AND EXCHANGE ACT OF 1934

       Date of Report (Date of earliest event reported): November 5, 2003

                                GERON CORPORATION

             (Exact name of registrant as specified in its charter)

            Delaware                     0-20859                 75-2287752
  (State or Other Jurisdiction   (Commission File Number)      (IRS Employer
       of Incorporation)                                  Identification Number)

          230 Constitution Drive                                     94025
          Menlo Park, California                                  (Zip Code)
 (Address of principal executive offices)

                                 (650) 473-7700
              (Registrant's telephone number, including area code)

          (Former Name or Former Address, if Changed Since Last Report)


Item 5.  Other Events.

On November 5, 2003, Geron Corporation announced that the underwriters of its
recent public offering of 5,000,000 shares of common stock have exercised their
over-allotment option in full to purchase 750,000 additional shares.

The Company's press release announcing the over-allotment exercise is filed as
an exhibit to this Current Report on Form 8-K. The summary description of the
event is qualified in its entirety by reference to the document filed as an
exhibit hereto.


Item 7.  Exhibits.

     99.1           Press Release dated November 5, 2003.



         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                GERON CORPORATION

Date:    November 5, 2003           By:     /s/ William D. Stempel
                                    Name:    William D. Stempel
                                    Title:   Vice President and General Counsel


                                  EXHIBIT INDEX

     99.1           Press Release dated November 5, 2003.