arXiv subjects

Anda Tenie

Publications and source records attributed to Anda Tenie.

5 recordsLinked to original sources

arXiv2026

Global smoothing of singular Fano and Calabi-Yau varieties

We study the problem of smoothing Fano and Calabi-Yau varieties with isolated Du Bois lci singularities. For Fano varieties, we show that any such $Y$ admits a deformation to a Fano variety with only $1$-rational singularities, and if none of the singularities of $Y$ are $1$-rational, then $Y$ is smoothable. For Calabi-Yau varieties, we show first that any such $Y$ deforms to a Calabi-Yau with only $1$-Du Bois singularities. Moreover, if none of the singularities of $Y$ are $1$-Du Bois then $Y$ is smoothable. When we allow $1$-liminal singularities, we give a global criterion in terms of the Hodge-Du Bois numbers of $Y$ which ensures that $Y$ is smoothable. These theorems recover and generalize results for threefolds of Friedman, Namikawa, Namikawa-Steenbrink, Gross, and Friedman-Laza. In higher dimensions, our results provide alternative smoothing conditions and also extend the work of Friedman-Laza from the case of rational hypersurface singularities to Du Bois lci singularities.

math.AG↗

arXiv2025

The integral chow ring of $M_2^{ct}$

This paper computes the integral Chow ring of the moduli space $M_2^{ct}$ of stable genus 2 curves of compact type. This is done by excising boundary strata from $\bar M_2$ one-by-one. During this process, we determine the Chow rings of all other open strata in $\bar M_2$ with $Z[1/2]$-coefficients.

math.AG↗

arXiv2024

Reider-type theorems on normal surfaces via Bridgeland stability

Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Our results still hold in positive characteristic or when $\omega_X \otimes L$ is not necessarily a line bundle. They also hold when the dualizing sheaf is replaced by a variant arising from the theory of Du Bois complexes. For complex surfaces with at most rational double point singularities, we recover the optimal bounds for global generation and very ampleness as predicted by Fujita's conjecture.

math.AG↗

arXiv2021

Strongly isospectral hyperbolic 3-manifolds with nonisomorphic rational cohomology rings

This paper shows that one cannot "hear" the rational cohomology ring of a hyperbolic 3-manifold. More precisely, while it is well-known that strongly isospectral manifolds have the same cohomology as vector spaces, we give an example of compact hyperbolic 3-manifolds that are strongly isospectral but have nonisomorphic rational cohomology rings. Along the way we implement a computer program which finds the nullity of the cup product map $H^1(M;\mathbb{Q})\wedge H^1(M;\mathbb{Q})\rightarrow H^2(M;\mathbb{Q})$ for any aspherical space in terms of the presentation of the fundamental group.

math.GT↗

arXiv2020

Graph coverings and (im)primitive homology: some new examples of exceptionally low degree

Given a finite covering of graphs $f : Y \to X$, it is not always the case that $H_1(Y;\mathbb{C})$ is spanned by lifts of primitive elements of $\pi_1(X)$. In this paper, we study graphs for which this is not the case, and we give here the simplest known nontrivial examples of covers with this property, with covering degree as small as 128. Our first step is focusing our attention on the special class of graph covers where the deck group is a finite $p$-group. For such covers, there is a representation-theoretic criterion for identifying deck groups for which there exist covers with the property. We present an algorithm for determining if a finite $p$-group satisfies this criterion that uses only the character table of the group. Finally, we provide a complete census of all finite $p$-groups of rank $\geq 3$ and order $< 1000$ satisfying this criterion, all of which are new examples.

math.GT↗