Tootfinder

Galois covers of Calabi-Yau manifolds
Matteo Verni
https://arxiv.org/abs/2507.14359 https://arxiv.org/pdf/2507.14359

Galois covers of Calabi-Yau manifolds
We study Galois rational maps between smooth projective varieties with trivial canonical bundle, with a particular interest in the case where the codomain is Hyper-Kähler. We obtain results about the birational geometry and the Galois closure of rational maps between Calabi-Yau manifolds. We apply these general results to a number of well-known examples.

Serre's question on thin sets in projective space
Tijs Buggenhout, Raf Cluckers, Tim Santens, Floris Vermeulen
https://arxiv.org/abs/2506.13471 https:/…

Serre's question on thin sets in projective space
We answer a question of Serre on rational points of bounded height on projective thin sets in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely corresponding to the images of ramified dominant quasi-finite covers of projective space, as thin sets of type I are already well understood via dimension growth results. We obtain a uniform affine variant of Serre's question which implies the projective case and for which t…

A Framework for Creating Non-Regressive Test Cases via Branch Consistency Analysis Driven by Descriptions
Yuxiang Zhang, Pengyu Xue, Zhen Yang, Xiaoxue Ren, Xiang Li, Linhao Wu, Jiancheng Zhao, Xingda Yu
https://arxiv.org/abs/2506.07486

A Framework for Creating Non-Regressive Test Cases via Branch Consistency Analysis Driven by Descriptions
Automated test-generation research overwhelmingly assumes the correctness of focal methods, yet practitioners routinely face non-regression scenarios where the focal method may be defective. A baseline evaluation of EvoSuite and two leading Large Language Model (LLM)-based generators, namely ChatTester and ChatUniTest, on defective focal methods reveals that despite achieving up to 83% of branch coverage, none of the generated tests expose defects. To resolve this problem, we first construct …

Representation stability for moduli spaces of admissible covers
Megan Chang-Lee, Siddarth Kannan, Philip Tosteson
https://arxiv.org/abs/2506.22640 https://…

Representation stability for moduli spaces of admissible covers
We prove a representation stability result for the sequence of spaces $\overline M_{g, n}^A$ of pointed admissible $A$-covers of stable $n$-pointed genus-$g$ curves, for an abelian group $A$. For fixed genus $g$ and homology degree $i$, we give the sequence of rational homology groups $H_i(\overline{M}_{g, n}^A;\mathbb Q)$ the structure of a module over a combinatorial category, a la Sam--Snowden, and prove that this module is generated in degree at most $g + 5 i$. This implies that the generat…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Mainak Bhowmik, Mihai Putinar
https://arxiv.org/abs/2505.24425 https://ar…

The Multivariate Herglotz-Nevanlinna Class: Superresolution
Unique solutions of bounded, or equivalently, non-negative real part, holomorphic interpolation in several complex variables with finite prescribed data are very rare, with rational inner functions in a polydisk as the best understood examples. We analyze the continuity of global solutions as functions of the finite interpolation data in neighborhoods of elements distinguished by this uniqueness property. Our study covers rational inner functions in the polydisk and automorphisms of the Euclide…