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HYPERBOLA METHOD ON TORIC VARIETIES

Marta Pieropan

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Ecole Polytechnique2024

A smooth compactification of the space of genus two curves in projective space: via logarithmic geometry and Gorenstein curves

Francesca Carocci

We construct a modular desingularisation of (M) over bar (2,n)(P-r, d)(main). The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers; with this enhanced logarithmic structure, it is possible to desi ...

GEOMETRY & TOPOLOGY PUBLICATIONS2023

FIBERED TORIC VARIETIES

Leonid Monin

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class ...

Independent Univ Moscow-Ium2023

Bundle-Specific Axon Diameter Index as a New Contrast to Differentiate White Matter Tracts

Jean-Philippe Thiran, Alessandro Daducci, Gabriel Girard, Cristina Granziera, David Paul Roger Romascano, Maxime Descoteaux, Muhamed Barakovic, Giorgio Innocenti

In the central nervous system of primates, several pathways are characterized by different spectra of axon diameters. In vivo methods, based on diffusion-weighted magnetic resonance imaging, can provide axon diameter index estimates non-invasively. However ...

2021

Three-dimensional fabrication of sub-micron optical waveguides in PDMS and other polymer materials

Giulia Panusa

Optical waveguides are one of the most important photonic components. They are indispensable tools in many of todayâ s technologies because of their capacity of guiding light. In particular, compact, low loss, flexible polymer optical waveguides are cruci ...

EPFL2021

Arithmetically rigid schemes via deformation theory of equivariant vector bundles

Maciej Emilian Zdanowicz

We analyze the deformation theory of equivariant vector bundles. In particular, we provide an effective criterion for verifying whether all infinitesimal deformations preserve the equivariant structure. As an application, using rigidity of the Frobenius ho ...

SPRINGER HEIDELBERG2021

Positivity of the CM line bundle for families of K-stable klt Fano varieties

Zsolt Patakfalvi, Giulio Codogni

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle ...

2021

Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0

Lei Zhang, Zsolt Patakfalvi

Let k be an algebraically closed field of characteristic p > 0. We give a birational characterization of ordinary abelian varieties over k: a smooth projective variety X is birational to an ordinary abelian variety if and only if kappa(S)(X) = 0 and b(1)(X ...

DUKE UNIV PRESS2019

Characteristic classes as complete obstructions

Martina Rovelli

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a sin ...

SPRINGER HEIDELBERG2019

On subadditivity of Kodaira dimension in positive characteristic over a general type base

Zsolt Patakfalvi

We show that for a surjective, separable morphism f of smooth projective varieties over a field of positive characteristic such that f(*) OX congruent to O-Y subadditivity of Kodaira dimension holds, provided the base is of general type and the Hasse-Witt ...

2018

A Looping-Delooping Adjunction For Topological Spaces

Martina Rovelli

Every principal G-bundle over X is classified up to equivalence by a homotopy class X -> BG, where BG is the classifying space of G. On the other hand, for every nice topological space X Milnor constructed a strict model of its loop space (Omega) over tild ...

Int Press Boston, Inc2017

Towards new invariants for principal bundles

Martina Rovelli

We investigate the theory of principal bundles from a homotopical point of view. In the first part of the thesis, we prove a classification of principal bundles over a fixed base space, dual to the well-known classification of bundles with a fixed structur ...

EPFL2017

Equivariant measurable liftings

Nicolas Monod

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Mobius group of the projective line. Since the general proof is very simple but not explicit, we also provi ...

Polish Acad Sciences Inst Mathematics-Impan2015

The xi-stability on the affine grassmannian

Zongbin Chen

We introduce a notion of xi-stability on the affine grassmannian (SIC) for the classical groups, this is the local version of the xi-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient ( ...

Springer Heidelberg2015

Dendrimer-Stabilized Titanate Nanowire Dispersions as Potential Nanocarriers

László Forró, Endre Horvath

The effect of poly(amido amine) (PAMAM) dendrimers of generations G2, G6, and G10 on the dispersion stability of titanate nanowires (TiONWs) as potential nanocarriers was clarified in order to develop biocompatible delivery systems. The PAMAMs adsorbed str ...

Amer Chemical Soc2015

Conjugation spaces and equivariant Chern classes

Jérôme Scherer

Let eta be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU has a canonical structure of a conjugation space, as defined ...

Belgian Mathematical Soc Triomphe2013

An actin length threshold regulates adhesion maturation at the lamellipodium/lamellum interface

Jean-Jacques Meister, Benoît Vianay, Céline Jeanne Labouesse

The mechanical coupling between adherent cells and their substrates is a major driver of downstream behavior. This coupling relies on the formation of adhesion sites and actin bundles. How cells generate these elements remains only partly understood. A pot ...

Royal Soc Chemistry2013

Balanced metrics on vector bundles and polarized manifolds

Mario Garcia Fernandez

We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter alpha, where X is a smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of alpha, we prove that the l ...

Oxford University Press2013

Invariant frames for vector bundles and applications

Tudor Ratiu, Madeleine Jotz

This paper completes a proof of the Dirac reduction theorem by involutive tangent subbundles. As a consequence, Dirac reduction by a proper Lie group action having one isotropy type is carried out. The main technical tool in the proof is the notion of part ...

Springer Verlag2012

Boiling on a Tube Bundle: Part I-Flow Visualization and Onset of Dryout

John Richard Thome, Navid Borhani, Eugene van Rooyen

A novel visualization method was developed and implemented in a refrigerant-flooded evaporator tube bundle. Specifically, a method to visualize the two-phase flow inside plain tube bundles was developed using a dummy tube with a tubular glass section for v ...

2012