Izzet Coskun

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We establish a positive geometric rule for computing the structure constants of the cohomology of two-step flag varieties with respect to their Schubert basis. As a corollary we obtain a quantum LittlewoodRichardson rule for Grassmannians. These rules have numerous applications to geometry, representation theory and the theory of symmetric functions.
In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps M0,0(P , d) stabilize when r ≥ d. We give a complete characterization of the effective divisors on M0,0(P, d): They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.
We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hypersurface in Pn of degree 2d ≤ min(n+4, 2n−2) and dimension at least three is irreducible and of the(More)
A Schubert class in the Grassmannian is rigid if the only proper subvarieties representing that class are Schubert varieties. The hyperplane class σ1 is not rigid because a codimension one Schubert cycle can be deformed to a smooth hyperplane section. In this paper, we show that this phenomenon accounts for the failure of rigidity in Schubert classes. More(More)
This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert(More)
We produce ample, respectively NEF, eventually free, divisors in the Kontsevich space M0,n(P , d) of n-pointed, genus 0, stable maps to Pr, given such divisors in M0,n+d. We prove this produces all ample, respectively NEF, eventually free, divisors in M0,n(P, d). As a consequence, we construct a contraction of the boundary ∪ bd/2c k=1 ∆k,d−k in M0,0(P r, d)(More)