Related papers: Free curves and fundamental groups

For a Fano threefold admitting a full exceptional collection of vector bundles of length four we show that all full exceptional collections consist of shifted vector bundles. We prove this via a detailed study of the group generated by…

Building on results of Clemens and Kley, we find criteria for a continuous family of curves in a nodal $K$-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation $Y_t$ of $Y_0$. As an…

In this note we make progress toward a conjecture of Durham--Fanoni--Vlamis, showing that every infinite-type surface with finite-invariance index 1 and no nondisplaceable compact subsurfaces fails to have a good curve graph, that is, a…

Tevelev degrees in Gromov-Witten theory are defined whenever there are virtually a finite number of genus $g$ maps of fixed complex structure in a given curve class $\beta$ through $n$ general points of a target variety $X$. These virtual…

We classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Pl\"ucker polarization) and study the fixed loci.

We study projective curves and hypersurfaces defined over a finite field that are tangent to every member of a class of low-degree varieties. Extending 2-dimensional work of Asgarli, we first explore the lowest degrees attainable by smooth…

In this article, we introduce an approach to study the fundamental group of a log terminal T-variety. As applications, we prove the simply connectedness of the spectrum of the Cox ring of a complex Fano variety, we compute the fundamental…

The variety of minimal rational tangents associated to Hecke curves was used by J.-M.Hwang [8] to prove the simplicity of the tangent bundle on the moduli of vector bundles over a curve. In this paper, we use the tangent maps of the…

In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for…

A Seifert surface F for a knot K is free if the complement of F is a handlebody (i.e., has free fundamental group). The free genus of K is the minimum genus among all free Seifert surfaces for K. In this paper we show that there exist…

We give a formula relating the total Tjurina number and the generic splitting type of the bundle of logarithmic vector fields associated to a reduced plane curve. By using it, we give a characterization of nearly free curves in terms of…

We prove that the derived category $D(C)$ of a generic curve of genus greater than one embeds into the derived category $D(M)$ of the moduli space $M$ of rank two stable bundles on $C$ with fixed determinant of odd degree.

In this article, we study the K-moduli space of Fano threefolds obtained by blowing up $\mathbb{P}^3$ along $(2,3)$-complete intersection curves. This K-moduli space is a two-step birational modification of the GIT moduli space of…

This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…

In this note, we give a so-called representative classification for the strata by automorphism group of smooth $\bar{k}$-plane curves of genus $6$, where $\bar{k}$ is a fixed separable closure of a field $k$ of characteristic $p = 0$ or $p…

In this paper, we investigate Fano manifolds whose Chern characters satisfy some positivity conditions. We prove that such manifolds admit long chains of higher order minimal families of rational curves and are covered by higher rational…

We study the local differential geometry of varieties $X^n\subset \Bbb C\Bbb P^{n+a}$ with degenerate secant and tangential varieties. We show that the second fundamental form of a smooth variety with degenerate tangential variety is…

Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over $\mathbb C$, in terms of purity properties of ultraproducts of characteristic $p$ Frobenii. The first…

We show how locally smooth actions of compact Lie groups on a manifold $X$ can be used to obtain new upper bounds for the topological complexity $\TC(X)$, in the sense of Farber. We also obtain new bounds for the topological complexity of…

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly…