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Torsten Ekedahl, Sergei Lando, Michael Shapiro, and Alek Vainshtein âˆ— Dept. of Math., University of Stockholm, S-10691, Stockholm, teke@matematik.su.se â€ Higher College of Math., Independent University of Moscow, and Institute for System Research RAS, lando@mccme.ru â€¡ Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm,â€¦ (More)

The enumeration of points on (or off) the union of some linear or affine subspaces over a finite field is dealt with in combinatorics via the characteristic polynomial and in algebraic geometry via the zeta function. We discuss the basic relations between these two points of view. Counting points is also related to the l-adic cohomology of the arrangementâ€¦ (More)

In this paper we find an explicit formula for the number of topologically different ramified coverings C â†’ CP 1 (C is a compact Riemann surface of genus g) with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.

- Torsten Ekedahl, Yuri Ivanovich
- 2002

We introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarised abelian variety in positive characteristic and study its geometric properties like irreducibility of the strata and we calculate the cycle classes. When the characteristic p is treated as a formal variable these classes can be seen asâ€¦ (More)

- Torsten Ekedahl
- 2003

We give upper and lower bounds for the order of the top Chern class of the Hodge bundle on the moduli space of principally polarized abelian

- Alex DEGTYAREV, Torsten Ekedahl, Ilia ITENBERG, Boris Z. Shapiro, Michael Shapiro
- 2006

â€” We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image. RÃ©sumÃ©. â€” On montre que, si tous les points critiques dâ€™une fonction mÃ©romorphe de degrÃ© au plus quatre sur uneâ€¦ (More)

It was earlier conjectured by the second and the third authors that any rational curve Î³ : CP â†’ CPn such that the inverse images of all its flattening points lie on the real line RP âŠ‚ CP is real algebraic up to a MÃ¶bius transformation of the image CPn, see [1], [8] and [12]. (By a flattening point p on Î³ we mean a point at which the Frenet n-frame (Î³, Î³, .â€¦ (More)

- Torsten Ekedahl
- 2008

We give an explicit construction, for a flat map X â†’ S of algebraic spaces, of an ideal in the nâ€™th symmetric product of X over S. Blowing up this ideal is then shown to be isomorphic to the schematic closure in the Hilbert scheme of length n subschemes of the locus of n distinct points. This generalises Haimanâ€™s corresponding result ([13]) for the affineâ€¦ (More)

âˆ— Dept. of Math., University of Stockholm, S-10691, Stockholm, teke@matematik.su.se â€ Higher College of Math., Independent University of Moscow, and Institute for System Research RAS, lando@mccme.ru â€¡ Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, mshapiro@math.kth.se â™® Dept. of Math. and Dept. of Computer Science, Universityâ€¦ (More)

- Torsten Ekedahl
- 2004

We give a generalization to higher genera of the famous formula 12 Î» = Î´ for genus 1. We also compute the classes of certain strata in the Satake compactification as elements of the push down of the tautological ring.