Related papers: Pullbacks of universal Brill-Noether classes via A…

In this paper we compare different notions of transversality for possible singular complex algebraic or analytic subsets of an ambient complex manifold and prove a refined intersection formula for their Chern-Schwartz-MacPherson classes. In…

We bound from below the complexity of the top Chern class of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section…

An Ulrich sheaf on an embedded projective variety is a normalized arithmetically Cohen-Macaulay sheaf with the maximum possible number of independent sections. Ulrich sheaves are important in the theory of Chow forms, Boij-Soderberg theory,…

We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how…

We calculate the orbifold Euler characteristics of all the degree d fine universal compactified Jacobians (defined by Pagani and Tommasi) over the moduli space of stable curves of genus g with n marked points. We show that this orbifold…

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on…

Let X be a smooth projective variety of dimension n. If $p+q=n+1$ then Bloch has defined a ${\bf G}_m$-biextension E over the product of the Chow groups $CH^p_0(X)$ and $CH^q_0(X)$ of homologically trivial cycles. We prove that E is the…

A map from the higher arithmetic $K$-group defined by the author to the higher arithmetic Chow group constructed by Burgos and Feliu is given. It is a higher extension of the arithmetic Chern character established by Gillet and Soul\'{e},…

The moduli space of principally polarized abelian varieties $A_g$ of genus g is defined over the integers and admits a minimal compactification $A_g^*$, also defined over the integers. The Hodge bundle over $A_g$ has its Chern classes in…

We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers $d$ and $r$, consider the variety $V^r_d(|H|)$ parametrizing curves $C$ in the…

We establish the twisted functoriality in nonabelian Hodge theory in positive characteristic. As an application, we obtain a purely algebraic proof of the fact that the pullback of a semistable Higgs bundle with vanishing Chern classes is…

We study the theta divisor of the compactified jacobian of a nodal, possibly reducible, curve. We compute its irreducible components and give it a geometric interpretation consistent with the classical Brill-Noether theory of smooth curves.…

Let X be a minuscule Schubert variety and $\alpha$ a class of 1-cycle on X. In this article we describe the irreducible components of the scheme of morphisms of class $\alpha$ from a rational curve to X. The irreducible components are…

In the paper ``Weil transfer of algebraic cycles'', published by the second author in Indagationes Mathematicae about 25 years ago, a Weil transfer map for Chow groups of smooth algebraic varieties has been constructed and its basic…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$.…

Let $C$ be a nodal curve and $L$ be an invertible sheaf on $C$. Let $\alpha_{L}:C\dashrightarrow J_{C}$ be the degree-$1$ rational Abel map, which takes a smooth point $Q\in C$ to $\left[ m_{Q}\otimes L\right] $ in the Jacobian of $C$. In…

We show that the smooth theta divisors of general principally polarised abelian varieties can be chosen as irreducible algebraic representatives of the coefficients of the Chern-Dold character in complex cobordisms and describe the action…

Based on Balmer's tensor triangular Chow group [2], we propose (Milnor)K-theoretic Chow groups of derived categories of schemes. These Milnor K-theoretic Chow groups recover the classical ones [6] for smooth projective varieties and can…

The double ramification (DR) cycle associated to a line bundle on a family of curves detects where the line bundle becomes fibrewise-trivial. The Hodge-DR Conjecture proposes a formula for powers of the first Chern class of a natural line…

Let X --> P^2 be a p-cyclic cover branched over a smooth, connected curve C of degree divisible by p, defined over a separably closed field of prime-to-p characteristic. We show that all (unramified) p-torsion Brauer classes on X that are…