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### How many linear varieties are contained in a projective variety?

**Special Events**

Speaker: | Jason Starr, Stony Brook University. |

Location: | 2112 MSB |

Start time: | Fri, Jan 14 2011, 3:00PM |

For a closed subvariety of projective space which is smooth, how many linear d-dimensional varieties are contained in the subvariety? If there are infinitely many, what is the dimension of the parameter space? If we deform the subvariety, how does the answer change? How many linear subvarieties are contained in the subvariety and contain a fixed, general point? I will discuss some recent work (primarily by Beheshti, but also some work of my own) motivated by a conjecture of Debarre and de Jong: every smooth, Fano hypersurface contains precisely the dimension of lines as "expected".