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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 |
Description
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".