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Yves Laszlo

Publications and source records attributed to Yves Laszlo.

15 recordsLinked to original sources
arXiv2012

Travaux de Gabber sur l'uniformisation locale et la cohomologie etale des schemas quasi-excellents. Seminaire a l'Ecole polytechnique 2006--2008

This book contains notes of a seminar on Ofer Gabber's work on the etale cohomology and uniformization of quasi-excellent schemes. His main results include (cf. introduction) constructibility theorems (for abelian or non-abelian coefficients), vanishing theorems (e.g. affine Lefschetz), uniformization for the "prime-to-l alteration topology", rigidity for non-abelian coefficients, a new proof of the absolute purity conjecture, duality, etc.

math.AG↗
arXiv2012

On the monodromy of the Hitchin connection

For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l different from 1,2,4 and 8 contains an element of infinite order.

math.AG↗
arXiv2006

Perverse sheaves on Artin stacks

In this paper we develop the theory of perverse sheaves on Artin stacks continuing the study in "The six operations for sheaves on Artin stacks I: Finite Coefficients" and "The six operations for sheaves on Artin stacks II: Adic Coefficients" (math.AG/0512097 and math.AG/0603680)

math.AG↗
arXiv2004

Estimates of Characteristic numbers of real algebraic varieties

We give some explicit bounds for the number of cobordism classes of real algebraic manifolds of real degree less than $d$, and for the size of the sum of $\mod 2$ Betti numbers for the real form of complex manifolds of complex degree less than $d$.

math.AG↗
arXiv2002

The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3

Let X be a smooth projective curve of genus g>1 defined over an algebraically closed field k of characteristic p>0. Let M_X(r) be the moduli space of semi-stable rank r vector bundles with fixed trivial determinant. The relative Frobenius map F : X \to X_1 induces by pull-back a rational map V: M_{X_1}(r) \to M_X(r). We determine the equations of V in the following two cases (1) (g,r,p) = (2,2,2) and X non-ordinary with Hasse-Witt invariant equal to 1 (see math.AG/0005044 for the case X ordinary), and (2) (g,r,p) = (2,2,3). We also show, for any triple (g,r,p), the existence of base points of V, i.e., semi-stable bundles E such that F^* E is not semi-stable.

math.AG↗
arXiv2000

On the Hitchin morphism in positive characteristic

Let X be a smooth projective curve over a field of characteristic p>0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a non-trivial deformation over the affine line. This deformation is constructed by considering the moduli stack of t-connections on vector bundles on X and an analogue of the p-curvature, and by observing that the associated characteristic polynomial is, in a suitable sense, a p-th power.

math.AG↗
arXiv2000

The action of the Frobenius map on rank 2 vector bundles in characteristic 2

Let $X$ be an ordinary smooth curve defined over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the moduli space $M_X$ of rank 2 vector bundles with fixed trivial determinant. If the genus of $X$ is 2, the moduli space $M_X$ is isomorphic to projective space of dimension 3 (as over the complex numbers). In this case we explicitly give the equations of $F$, which enables us to determine, for example, its base locus (one point) and its image (different from $M_X$).

math.AG↗
arXiv1996

The Picard group of the moduli of G-bundles on a curve

Let G be a complex semi-simple group, and X a compact Riemann surface. The moduli space of principal G-bundles on X, and in particular the holomorphic line bundles on this space and their global sections, play an important role in the recent applications of Conformal Field Theory to algebraic geometry. In this paper we determine the Picard group of this moduli space when G is of classical or G_2 type (we consider both the coarse moduli space and the moduli stack).

alg-geom↗
arXiv1996

The line bundles on the stack of parabolic $G$-bundles over curves and their sections

Let $X$ be a smooth, complete and connected curve and $G$ be a simple and simply connected algebraic group over $\comp$. We calculate the Picard group of the moduli stack of quasi-parabolic $G$-bundles and identify the spaces of sections of its members to the conformal blocs of Tsuchiya, Ueno and Yamada. We describe the canonical sheaf on these stacks and show that they admit a unique square root, which we will construct explicitly. Finally we show how the results on the stacks apply to the coarse moduli spaces and recover (and extend) the Drezet-Narasimhan theorem. We show moreover that the coarse moduli spaces of semi-stable $SO_r$-bundles are not locally factorial for $r\geq 7$.

alg-geom↗
arXiv1994

Local structure of the moduli space of vector bundles over curves

We analyze the local structure of the moduli space of semi-stable bundles on a curve. In particular, a complete description of the local structure is given in the rank 2 case. We obtain as a corollary of this analysis new results about the Kummer variety and the Coble quartic associated to a canonical genus 3 curve.

alg-geom↗
arXiv1993

Conformal blocks and generalized theta functions

Let M(r) be the moduli space of rank r vector bundles with trivial determinant on a Riemann surface X . This space carries a natural line bundle, the determinant line bundle L . We describe a canonical isomorphism of the space of global sections of L^k with a space known in conformal field theory as the ``space of conformal blocks", which is defined in terms of representations of the Lie algebra sl(r, C((z))).

alg-geom↗