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We study the codimension two locus $H$ in $𝒜_{g}$ consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class $[H] \in C H^{2} (𝒜_{g})$ for every $g$ . For $g = 4$ , this turns out to be the locus of Jacobians with a vanishing theta-null. For $g = 5$ , via the Prym map we show that $H \subset 𝒜_{5}$ has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of $\bar{𝒜_{5}}$ and show that the component $\bar{N_{0}^{'}}$ of the Andreotti-Mayer...

Singularities on complete algebraic varieties

Fedor Bogomolov, Paolo Cascini, Bruno Oliveira (2006)

Open Mathematics

We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.

Singularities on flag spaces

Miloš Božek, Konrad Drechsler (1999)

Mathematica Slovaca

Singularities with exact Poincaré complex but not quasihomogeneous.

Gerhard Pfister, Hans Schönemann (1989)

Revista Matemática de la Universidad Complutense de Madrid

We give examples of complete intersections in C3 with exact Poincaré complex but not quasihomogeneous using the classification of C.T.C. and the algorithm of Mora.

Singularity of the moduli space of stable bundles on surfaces

Tohru Nakashima (1996)

Compositio Mathematica

Skew fields of noncommutative rational functions (preliminary version)

George W. Bergman (1969/1970)

Séminaire Schützenberger

Skew-Symmetric Vanishing Lattices and Their Monodromy Groups.

W.A.M. Janssen (1984)

Mathematische Annalen

Skew-Symmetric Vanishing Lattices and Their Monodromy Groups. II.

W.A.M. Janssen (1985)

Mathematische Annalen

${SL}_{2}$ -equivariant polynomial automorphisms of the binary forms

Alexandre Kurth (1997)

Annales de l'institut Fourier

We consider the space of binary forms of degree $n \geq 1$ denoted by $R_{n} : = ℂ [x, y]_{n}$ . We will show that every polynomial automorphism of $R_{n}$ which commutes with the linear ${SL}_{2} (ℂ)$ -action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on $R_{n}$ .

SL2 actions and cohomology of Schubert varieties

E. Akyildiz (1990)

Banach Center Publications

SL2-triplet associé à un polynôme homogène.

H. Rubenthaler, G. Schiffmann (1990)

Journal für die reine und angewandte Mathematik

Slices and transfers.

Levine, Marc (2010)

Documenta Mathematica

Slices étales

Domingo Luna (1973)

Mémoires de la Société Mathématique de France

Slope filtration of quasi-unipotent overconvergent $F$ -isocrystals

Nobuo Tsuzuki (1998)

Annales de l'institut Fourier

We study local properties of quasi-unipotent overconvergent $F$ -isocrystals on a curve over a perfect field of positive characteristic $p$ . For a $φ$ - $\nabla$ -module over the Robba ring $ℛ$ , we define the slope filtration for Frobenius structures. We prove that an overconvergent $F$ -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.

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Singularities of polar curves

Singularities of Quotients by Vector Fields in Characteristic p.

Singularities of the moduli spaces of certain abelian surfaces

Singularities of theta divisors and the geometry of $𝒜_{5}$