Tootfinder

Pencils of projective hypersurfaces, Griffiths heights and geometric invariant theory. II Hypersurfaces with semihomogeneous singularities
Thomas Mordant
https://arxiv.org/abs/2506.22126

Pencils of projective hypersurfaces, Griffiths heights and geometric invariant theory. II Hypersurfaces with semihomogeneous singularities
This paper establishes the formula for the stable Griffiths height of the middle-dimensional cohomology of a pencil of projective hypersurfaces $H$, with semihomogeneous singularities, over some smooth projective curve $C$, that appears as Theorem 5.1 in the first part of this paper (arxiv:2506.15334). The proof of this formula relies on the strategy developed in my previous work (arxiv:2212.11019v3) to derive an expression for this Griffiths height when the only singularities of the fibers o…

Painted into a Corner: Cowboys suffer another injury at CB; team thin on options https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/07/29/cowboys-cb-caelen-carson-hyperextended-knee/85428228007/

This https://arxiv.org/abs/2412.17410 has been replaced.
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Rigidity of spacelike hypersurface with constant curvature and intersection angle condition
In the Minkowski space, we consider a spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. This result can be seen as an analog of the sphere theorem for the hypersurface of constant $k$-th mean curvature in the Euclide…

Lipschitz geometry of the image of finite mappings
Juan Jos\'e Nu\~no Ballesteros, Vin\'icius de Oliveira Prado, Guillermo Pe\~nafort Sanchis, Jos\'e Edson Sampaio
https://arxiv.org/abs/2507.21405

Lipschitz geometry of the image of finite mappings
This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if the multiplicity of $f$ is equal to his generic degree, then the image of $f$ is LNE at 0 if and only if it is a smooth germ. We also show that every finite corank 1 map is sattisfies the previous hypothesis. Moreover, we show that for an injective map germ $f…

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The Red and Yellow Hypergiants
Terry Jones
https://arxiv.org/abs/2507.15962 https://arxiv.org/pdf/2507.15962

The Red and Yellow Hypergiants
The red and yellow hypergiants are a rare and important phase in the evolution of the most massive stars that can reach the cool part of the HR Diagram. The hypergiant phase is commonly characterized by high, often episodic mass-loss rates and significant changes in spectral type, probably due to the formation of a pseudo photopsphere during a high mass-loss episode. Many of the yellow hypergiants are the immediate successors to the most luminous red supergiants, and often show evidence in thei…

Overpartitions with parts separated by parity
Kathrin Bringmann, Catherine Cossaboom, William Craig
https://arxiv.org/abs/2507.16769 https://

Overpartitions with parts separated by parity
In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose parts are separated by parity, and we prove various $q$-series identities for these functions. These identities include relations to modular forms, $q$-hypergeometric series, and mock modular forms.

New examples of CR submanifolds for the $2$-jet determination problem
Florian Bertrand, Martin Kol\'a\v{r}, Francine Meylan
https://arxiv.org/abs/2506.21221

New examples of CR submanifolds for the $2$-jet determination problem
This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension $7$ in $\mathbb{C}^{10}$ that is not strictly pseudoconvex and for which its germs of …

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
Daniel V. Leibovici, Oscar P. Bruno
https://arxiv.org/abs/2506.19370

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation of the scheme with high-quality weak and strong scalability properties, and it illustrates the overall methodology for a variety of tests for the 2D Euler equations--including supersonic and hypersonic flows and shocks past obstacles with corners. The result…

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