The California High Speed Rail Authority has been workshopping route details all over the state. Especially sensitive are the Atherton/Menlo Park/Palo Alto areas and the area immediately to the south of Diridon Station, where numerous alternatives exist. In the picture below, you'll see a mix of working class residential and industrial buildings near the station. Further south is the well-heeled neighborhood of Willow Glen, and while the train wouldn't run through Willow Glen its residents are more than a bit concerned about HSR.
Unlike in the Peninsula, which the existing Caltrain corridor is the only available route, several route options exist south Diridon Station. CHSRA wants to use the most cost-effective route possible since they want to stretch the $10 billion in state bonds and whatever federal stimulus money comes their way, but every option has a cost/benefit component in both the short and long term.
The least expensive route is probably the green/white line above labeled SR87/I-280. It's an S-curve that would run in an aerial along the two area freeways. However, the S-curve makes it also the slowest option, and could adversely impact many of the express trains that would pass through San Jose without stopping at Diridon. The route also runs through the original Orchard Supply Hardware location's parking lot. Along with the other Caltrain-aligned routes, it would likely take some amount of land from the ballpark site. FWIW, that land wouldn't be for the ballpark anyway, it'd be used for parking.
The "Downtown Aerial/Tunnel" option is misleading because running an aerial isn't really an option. An aerial would require billions of dollars of eminent domain proceedings and would kill any chance of developing the six blocks between the ballpark site and the arena. A tunnel would be an enormous engineering challenge, since it would bore under both the existing light rail tunnel and the planned BART subway, plus a creek and a river. In either case, the route would have minimal impact on the ballpark site, clipping the northeast corner at worst.
However CHSRA and Diridon area residents proceed, it's good to know that the ballpark can be built without having to worry about the final route's impact.