1,720,983 research outputs found
Pluri-canonical models of supersymmetric curves
No full textThis paper is about pluri-canonical models of supersymmetric (susy) curves. Susy curves are generalisations of Riemann surfaces in the realm of super geometry. Their moduli space is a key object in supersymmetric string theory. We study the pluri-canonical models of a susy curve, and we make some considerations about Hilbert schemes and moduli spaces of susy curves
Hyperelliptic Schottky Problem and Stable Modular Forms
Full text linkIt is well known that, fixed an even, unimodular, positive definite quadratic form, one can construct a modular form in each genus; this form is called the theta series associated to the quadratic form. Varying the quadratic form, one obtains the ring of stable modular forms. We show that the differences of theta series associated to specific pairs of quadratic forms vanish on the locus of hyperelliptic Jacobians in each genus. In our examples, the quadratic forms have rank 24, 32 and 48. The proof relies on a geometric result about the boundary of the Satake compactification of the hyperelliptic locus. We also study the monoid formed by the moduli space of all principally polarised abelian varieties, the operation being the product of abelian varieties. We use this construction to show that the ideal of stable modular forms vanishing on the hyperelliptic locus in each genus is generated by differences of theta series
Corrigendum to “Non-reductive automorphism groups, the Loewy filtration and K-stability”
Full text linkNon-reductive automorphism groups, the Loewy filtration and K-stability
Full text linkWe study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several examples which we compute. We conjecture this holds in general. This is an algebro-geometric analogue of Matsushima’s theorem regarding the existence of constant scalar curvature Kähler metrics. As an application, we give an example of an orbifold del Pezzo surface without a Kähler-Einstein metric
DE CIFRIS SEMINARS
Full text linkDe Componendis Cifris APS was formally established only in December 2022, but it has been active for many years in meetings and events. One of its initiatives has been the organization of many seminars. It is therefore fitting that a Koine book collects some of our best seminars. Some results may be outdated, but the papers still provide valuable insights into many areas of cryptographic research and also serve as nice introductions. The volume concludes with two interesting and original contributions.
We believe that the volume’s editors, Danilo Bazzanella, Giulio Codogni, Nadir Murru and Roberto Zunino, have done a great job in selecting an interesting sample of seminars and two invited papers: isogeny-based post-quantum cryptography and integer factorization
The Gauss map and secants of the Kummer variety
Full text linkFay’s trisecant formula shows that the Kummer variety of the Jacobian of a smooth projectivecurve has a four-dimensional family of trisecant lines. We study when these lines intersect thetheta divisor of the Jacobian and prove that the Gauss map of the theta divisor is constant onthese points of intersection, when defined. We investigate the relation between the Gauss mapand multisecant planes of the Kummer variety as well
Torus equivariant K-stability
Full text linkIt is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds
On some modular contractions of the moduli space of stable pointed curves
Full text linkThe aim of this paper is to study some modular contractions of the moduli
space of stable pointed curves. These new moduli spaces, which are modular
compactifications of the moduli space of smooth pointed curves, are related
with the minimal model program for the moduli space of stable pointed curves
and have been introduced in a previous work of the authors. We interpret them
as log canonical models of adjoints divisors and we then describe the Shokurov
decomposition of a region of boundary divisors on the moduli space of stable
pointed curves.Comment: 30 pages, 1 figure. To appear on Algebra and Number Theor
The non-existence of stable Schottky forms
No full textWe show that there is no stable Siegel modular form that vanishes on every moduli space of curves
The degree of the Gauss map of the theta divisor
No full textWe study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. Thanks to this analysis, we obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus. We spell out this bound in several examples, and we use it to understand the local structure of isolated singular points. We further define a stratification of the moduli space of ppavs by the degree of the Gauss map. In dimension four, we show that this stratification gives a weak solution of the Schottky problem, and we conjecture that this is true in any dimension
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