viktorbb

• Barth, Viktor Balch; Hornslien, William; Quick, Gereon & Wilson, Glen Matthew (2025). Making the motivic group structure on the endomorphisms of the projective line explicit. Advances in Mathematics. ISSN 0001-8708. 461, s. 1–65. doi: 10.1016/j.aim.2024.110080. Fulltekst i vitenarkiv Vis sammendrag

  We construct a group structure on the set of pointed naive homotopy classes of scheme morphisms from the Jouanolou device to the projective line. The group operation is defined via matrix multiplication on generating sections of line bundles and only requires basic algebraic geometry. In particular, it is completely independent of the construction of the motivic homotopy category. We show that a particular scheme morphism, which exhibits the Jouanolou device as an affine torsor bundle over the projective line, induces a monoid morphism from Cazanave’s monoid to this group. Moreover, we show that this monoid morphism is a group completion to a subgroup of the group of scheme morphisms from the Jouanolou device to the projective line. This subgroup is generated by a set of morphisms that are very simple to describe.

• Barth, Viktor Balch & Truong, Trung Tuyen (2024). Images of dominant endomorphisms of affine space. Communications in Algebra. ISSN 0092-7872. doi: 10.1080/00927872.2024.2418374. Fulltekst i vitenarkiv
• Barth, Viktor Balch (2023). Surjective morphisms from affine space to its Zariski open subsets. International Journal of Mathematics. ISSN 0129-167X. 34(12). doi: 10.1142/S0129167X23500751. Fulltekst i vitenarkiv Vis sammendrag

  We prove constructively the existence of surjective morphisms from affine space onto certain open subvarieties of affine space of the same dimension. For any algebraic set [Formula: see text], we construct an endomorphism of [Formula: see text] with [Formula: see text] as its image. By Noether’s normalization lemma, these results extend to give surjective maps from any [Formula: see text]-dimensional affine variety [Formula: see text] to [Formula: see text].

Se alle arbeider i NVA

• Barth, Viktor Balch (2022). Surjective algebraic maps onto algebraically subelliptic manifolds. Fulltekst i vitenarkiv
• Barth, Viktor Balch (2021). Surjective algebraic maps onto algebraically subelliptic manifolds. Fulltekst i vitenarkiv

Se alle arbeider i NVA