For a moduli space $${\mathsf M}$$ of stable sheaves over K3 surface X, we propose series conjectural identities in the Chow rings $$CH_\star ({\mathsf M}\times X^\ell ),\, \ell \ge 1,$$ generalizing classic Beauville–Voisin identity for surface. We emphasize consequences conjecture structure tautological subring $$R_\star M}) \subset CH_\star M}).$$ The places all classes lowest piece natural ...

Let A be a commutative R–algebra of finite transcendence degree d ∈ N. We investigate the relationship between the subring of (geometrically) bounded elements H(A) := {a ∈ A | ∃ν ∈ N : |a| ≤ ν on SperA} and the subring of arithmetically bounded elements H (A) := {a ∈ A | ∃ν ∈ N : ν + a and ν − a are sums of squares in A}. Obviously, H ′(A) ⊆ H(A). In 1991, Schmüdgen proved the remarkable theore...

We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...

It is shown that any finitely generated subring of a global field has universal first-order definition in its fraction field. This covers Koenigsmann's result for the ring integers and subsequent extensions to rings number fields $S$-integers function odd characteristic. In this article proof presented which uniform all fields, including characteristic two case, where entirely novel. Furthermor...

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper. In this note we answer a question by Todorov and Vernaeve (see, e.g., [35]) concerning the relationship between the field of logarithmic-exponential series from [14] and the...

The ever increasing demand for interconnect bandwidth in embedded parallel processors has motivated the development of photonic communications technologies that effectively support short-distance links. Electrooptical I/O to and from VLSI chips is one such photonic technology. A multiring architecture that exploits optical I/O on and off chip is described in [1]. At the heart of the system is a...

For a finitely generated discrete group $\Gamma$ acting properly on spin manifold $M$, we formulate new topological obstructions to $\Gamma$-invariant metrics of positive scalar curvature $M$ that take into account the cohomology classifying space $\underline{B}\Gamma$ for proper actions. In cocompact case, this leads natural generalisation Gromov-Lawson's notion higher $\hat{A}$-genera setting...