The case pits Abigail Fisher against the University of Texas.
Ms Fisher, who is white, says her rights under the constitution's 14th Amendment were violated when she failed to get in. The university says that while it does indeed take race into account in selecting candidates, it does so as part of a "holistic" review fully consistent with the court's precedents, in particular Justice Sandra Day O'Connor's opinion in the landmark 2003 case, Grutter v. Bollinger.
Writing for a slim 5-4 majority Justice O'Connor held that the University of Michigan Law School's admissions strategy passed muster: it was adopted in "good faith", did not rely on demographically-based quotas and was "narrowly tailored" to "a compelling interest in attaining a diverse student body" with a "critical mass" of minority students.
Opponents of affirmative action would like to believe that, with Justice O'Connor's replacement by the far more conservative Justice Samuel Alito, there is now a critical mass on the court for banning race-based preferences altogether. They hope Ms Fisher will persuade a majority if not to reverse Grutter, then at least, in the words of Justice Sonia Sotomayor (who will not be part of that majority), "gut it".
There is a school of progressive thought which would not mind seeing Ms Fisher prevail. In a new study for The Century Foundation, Richard Kahlenberg looks at how universities have been handling diversity in the seven states, including California, where racial preferences have been already been banned by referenda, state legislatures or gubernatorial executive order. The news is good.
Responses include partnerships with disadvantaged schools, new race-neutral preferences for students from all difficult environments, no more automatic slots for offspring of alumni, and guaranteed places, regardless of test scores, for a fixed percentage of top students from all in-state public schools. Many of these are terrible, de facto segregated and disproportionately starved of resources.
"For people who care about social equality, all these new measures are intrinsically desirable," Kahlenberg writes. But they don't come naturally to university administrators because they are harder and more expensive to implement.
Research by Derek Bok, former president of Harvard, found that 86% of African Americans at universities with selective admissions standards were either middle or upper class. At Ivy League schools, 41% of black students were not even African American, but immigrants from relatively advantaged backgrounds.