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TWELVE POINTS ON THE PROJECTIVE LINE, BRANCHED COVERS, AND RATIONAL ELLIPTIC FIBRATIONS
PROJECTIVE LINE BRANCHED COVERS
2015/7/14
The following divisors in the space Sym12 P1 of twelve points on
P1 are actually the same: (A) the possible locus of the twelve nodal bers in
a rational elliptic bration (i.e. a pencil of plane cu...
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces
Lagrangian fibrations blowups of toric varieties mirror symmetry hypersurfaces Algebraic Geometry
2012/5/9
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface ...
Homotopy coherent diagrams and approximate fibrations
Approximate fibration homotopy coherence ENR
2011/9/21
Abstract: Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space ...
Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds.We first study monodromy representat...
Rational Fibrations of $\bar{M}_{5,1}$ and $\bar{M}_{6,1}$
Rational Fibrations $\bar{M}_{5,1}$ $\bar{M}_{6,1}$
2011/2/25
This is the second of two papers on the birational geometry ofM g,1. We construct rationalmaps fromM5,1 andM6,1 to lower-dimensional moduli spaces. As a consequence, we identify geometric divisors tha...
Convolutional Goppa codes defined on fibrations
Convolutional codes Goopa codes MDS codes finite fields
2011/2/25
We define a new class of Convolutional Codes in terms of fibrations of algebraic varieties generalizaing our previous constructions of Convolutional Goppa Codes ([1, 14]). Using this general construct...
Orthogonally spherical objects and spherical fibrations
Orthogonally spherical objects spherical fibrations
2010/11/9
We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D(Z x X) to be spherical over Z if the corresponding functor from D(Z) to D(X)...
Relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations
Relative Fourier-Mukai transforms Weierstrass fibrations
2010/11/15
We study the group of relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano or anti-Fano fibrations. For Weierstrass and Fano or anti-Fano fibrations we are able to d...
Lipschitz minimality of Hopf fibrations and Hopf vector fields
Lipschitz minimality Hopf fibrations Hopf vector fields
2010/12/14
Given a Hopf bration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range,the unique Lipschitz constant minimize...
Classifying spaces and fibrations of simplicial sheaves
classifying spaces fibre sequence simplicial sheaves
2010/12/7
In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a class...
Using Eliashberg's theorem about Stein fillings of S3 we prove that a section of a Lefschetz fibration over S2 has nonnegative square. This observation, in particular, implies that the identity elemen...
This paper has two essentially unrelated halves. In the first we prove that a closed symplectic four-manifold admitting a fibration by connected, homologically essential Lagrangian tori with "tame" si...
U(1)-invariant special Lagrangian 3-folds in {\mathbb C}3 and special Lagrangian fibrations
U(1)-invariant special Lagrangian 3-folds special Lagrangian fibrations
2010/3/1
This is a survey of the author's series of three papers [8, 9, 10] on special Lagrangian 3-folds (SL 3-folds) in {\mathbb C}3 invariant under the U(1)-action (z1,z2,z3)eiqz1, e-iqz2,z3), and their seq...
We argue that G2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M-five-brane fibers ...
Fiber sums of genus 2 Lefschetz fibrations
Lefschetz fibrations non-trivia l topologica l phenomena
2010/3/1
Using the recent results of Siebert and Tian about the holomorphicity of genus 2 Lefschetz fibrations with irreducible singular fibers, we show that any genus 2 Lefschetz fibration becomes holomorphic...