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1. Aluffi, P.

et al.

Faber, Carel

Plane curves with small linear orbits I2000In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 50, no 1, p. 151-+Article in journal (Refereed)

Abstract [en]

The linear orbit of a plane curve of degree d is its orbit in Pd(d+3)/2 under the natural action of PGL(3). In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for arbitrary plane curves. Linear orbits of smooth plane curves were studied by the authors in J. of Alg. Geom., 2 (1993), 155-184.

2. Ammann, Bernd

et al.

Dahl, Mattias

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

3.

Bjorklund, Michael

et al.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

Fish, Alexander

CONTINUOUS MEASURES ON HOMOGENOUS SPACES2009In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 59, no 6, p. 2169-2174Article in journal (Refereed)

Abstract [en]

In this paper we generalize Wiener's characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

4.

Chacholski, Wojciech

et al.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

Scherer, Jerome

Werndli, Kay

HOMOTOPY EXCISION AND CELLULARITY2016In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 66, no 6, p. 2641-2665Article in journal (Refereed)

Abstract [en]

Consider a push-out diagram of spaces C <- A -> B, construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object A. We compare the difference between A and this homotopy pull-back. This difference is measured in terms of the homotopy fibers of the original maps. Restricting our attention to the connectivity of these maps, we recover the classical Blakers-Massey Theorem.

5.

De Monvel, Anne Boutet

et al.

Univ Paris Diderot, Inst Math Jussieu PRG, F-75205 Paris 13, France..

Lenells, Jonatan

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Shepelsky, Dmitry

Inst Low Temp Phys, Math Div, UA-61103 Kharkov, Ukraine.;Kharkov Natl Univ, Sch Math & Comp Sci, UA-61022 Kharkov, Ukraine..

We analyze the long-time asymptotics for the Degasperis- Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated 3 x 3-matrix valued Riemann-Hilbert problem, we find an explicit formula for the leading order asymptotics of the solution in the similarity region in terms of the initial and boundary values.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Piene, Ragni

Higher order duality and toric embeddings2014In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 64, no 1, p. 375-400Article in journal (Refereed)

Abstract [en]

The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also describe the tropicalization of all higher order dual varieties of an equivariantly embedded (not necessarily normal) toric variety.

7.

Faber, Carel

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all g and n if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.

8.

Gulbrandsen, Martin G.

et al.

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties (A, Theta) of dimension g, by the existence of g + 2 points Gamma subset of A in special position with respect to 2 Theta, but general with respect to Theta, and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly nonreduced subschemes Gamma.

Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base Y degrees, and suppose the family is non-isotrivial. If Y is a smooth compactification of Y degrees, such that D : = Y \ Y degrees is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along D. Viehweg and Zuo have shown that for some m > 0, the mth symmetric power of this sheaf admits many sections. More precisely, the mth symmetric power contains an invertible sheaf whose Kodaira-Iitaka dimension is at least the variation of the family. We refine this result and show that this "Viehweg-Zuo sheaf" comes from the coarse moduli space associated to the given family, at least generically. As an immediate corollary, if Y degrees is a surface, we see that the non-isotriviality assumption implies that Y degrees cannot be special in the sense of Campana.

10.

Johansson, Kurt

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

The purpose of this article is to give, for any (commutative) ring A, an explicit minimal set of generators for the ring of multisymmetric functions TSAd[x(1),...,x(r)]) = (A[x(1),...,x(r)](circle times)A(d))8(d) A as an A-algebra. In characteristic zero, i.e. when A is a Q-algebra, a minimal set of generators has been known since the 19(th) century. A rather si-nall generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound oil the generators, improving the degree bound previously obtained by Fleischmann. As Gamma(d)(A) (A[x(1),...,x(r)]) = TSAd (A[x(1),...,x(r)]) we also obtain generators for di A vided powers algebras: If B is a finitely generated A-algebra with a given surjection A[x(1), x(2),...,x(r)] --> B then using the corresponding surjection Gamma(d)(A) (A[x(1),...,x(r)]) --> Gamma(d)(A) (B) we get generators for Gamma(d)(A) (B).