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We study the geometry of moduli spaces of genus 0 and 1 curves in Pn with speci ed contact with a hyperplane H. We compute intersection numbers on these spaces that correspond to the number of degre...
The following divisors in the space Sym12 P1 of twelve points on P1 are actually the same: (A) the possible locus of the twelve nodal bers in a rational elliptic bration (i.e. a pencil of plane cu...
We prove that the Chow quotient parametrizing configurations of n points in Pd which generically lie on a rational normal curve is isomorphic to M0,n, generalizing the well-known d = 1 result of Kapra...
In this paper we compute the number of rational curves with one node passing through a given number of points, lines and tangent to a given number of planes in P3.
We speculate about an algebro-geometric proof of Harer’s theorem on the rational Picard group of the moduli space of smooth complex curves. In particular, we refine the approach of Diaz and Edidin in-...
Rational Curves on K3 Surfaces      Rational  K3 Surfaces        2011/2/22
We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps an...
Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V , not equal to V , such tha...
grande, pour une classe d’´equations semilin´eaires avec des conditions p´eriodiques sur le bord: utt − uxx = f(x, u),u(0, t) = u(, t) , ux(0, t) = ux(, t).Notre m´etho...
When factoring linear partial di erential systems with a nite-dimensional solution space or analysing symmetries of nonlinear ODEs, we need to look for rational solutions of certain nonlinear PDEs. T...

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