Related papers: Deligne-Riemann-Roch and intersection bundles
In this note, we obtain a number of results related to the hard Lefschetz theorem for pseudoeffective line bundles, due to Demailly, Peternell and Schneider. Our first result states that the holomorphic sections produced by the theorem are…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…
Grothendieck's Esquisse d'un programme is often referred to for the ideas it contains on dessins d'enfants, the Teichm{\"u}ller tower, and the actions of the absolute Galois group on these objects or their etale fundamental groups. But this…
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential…
According to the decomposition and relative hard Lefschetz theorems, given a projective map of complex quasi projective algebraic varieties and a relatively ample line bundle, the rational intersection cohomology groups of the domain of the…
On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the…
Let M be a U(1) bundle over a smooth Riemann surface. I show that for Chern-Simons theory on M, with structure group G, the path integral is an integral over the space of G-connections on the Riemann surface involving characteristic classes…
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical…
We study systems involving vector bundles and logarithmic connections on Riemann surfaces and linear algebra data linking their residues. This generalizes representations of deformed preprojective algebras. Our main result is the existence…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
We prove that a system of equations introduced by Demailly (to attack a conjecture of Griffiths) has a smooth solution for a direct sum of ample line bundles on a Riemann surface. We also reduce the problem for general vector bundles to an…
This is the sequel of the first part math.DG/0611281. Here, the procedure of transgressing the families index theorem (the so-called $\eta$-form) is adapted to take in account the case of Dirac type operators with kernels of varying…
We explain how to construct a cohomology theory on the category of separated quasi-compact smooth rigid spaces over $\mathbf{C}_p$ (or more general base fields), taking values in the category of vector bundles on the Fargues-Fontaine curve,…
In this paper we construct arithmetic analogs of the Riemann-Roch theorem and Serre's duality for line bundles. This improves on the works of Tate and van der Geer - Schoof. We define $H^0(L)$ and $H^1(L)$ as some convolution of measures…
We give an informal exposition of pushforwards and orientations in generalized cohomology theories in the language of spectra. The whole note can be seen as an attempt at convincing the reader that Todd classes in…
We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott. Then we consider the direct image of a…
This is the second part of a series of papers which bridges the Chang--Weinberger--Yu relative higher index and geometry of almost flat hermitian vector bundles on manifolds with boundary. In this paper we apply the description of the…
Inspired by the work of Ulrich and Huneke-Ulrich, we describe a pattern to show that the ideals of certain opposite embedded Schubert varieties defined by this pattern arise by taking residual intersections of two geometrically linked…
In this lecture we review apprearance of the Riemann-Roch Theorem in classical function theory, Algebraic topology, in theory of pseudo-differential operators and finally in noncommutative geometry. We show also it usefulness in many…