Geodesic
Real rational curves in Grassmannians
Sottile, Frank1, 2
1 Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
2 Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-4515
Journal of the American Mathematical Society, Tome 13 (2000) no. 2, pp. 333-341 Cet article a éte moissonné depuis la source American Mathematical Society

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Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some given general figures. For the problem of plane conics tangent to five general (real) conics, the surprising answer is that all 3264 may be real. Similarly, given any problem of enumerating $p$-planes incident on some given general subspaces, there are general real subspaces such that each of the (finitely many) incident $p$-planes is real. We show that the problem of enumerating parameterized rational curves in a Grassmannian satisfying simple (codimension 1) conditions may have all of its solutions real.
DOI : 10.1090/S0894-0347-99-00323-9

Sottile, Frank 1, 2

1 Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
2 Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-4515 
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Sottile, Frank. Real rational curves in Grassmannians. Journal of the American Mathematical Society, Tome 13 (2000) no. 2, pp. 333-341. doi: 10.1090/S0894-0347-99-00323-9

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