Kate,
You can buy Loctite 420 online, but it is not cheap then buy a couple syringes at your pharmacy. A needle is necessary to get it in deep, fill the crack and let it dry. Use blade scrape flat, refill if needed. Next day scrap smooth, then sand with 220, 400 and 600 garnet paper. Wet sanding with 600 will smooth it out nicely, then you can put a little Polyurethane on with a brush. If you want to do more you can.
Loctite has a website, where you can print out info on this product.