arXiv subjects

Ana Julisa Palomino

Publications and source records attributed to Ana Julisa Palomino.

4 recordsLinked to original sources

arXiv2026

Quotients of Calabi-Yau Generalized Fermat manifolds and Log Enriques varieties

Enriques manifolds and Log Enriques varieties have attracted a lot of interest in the last years. In this paper we study Enriques manifolds and Log Enriques varieties that are respectively étale and quasi-étale quotients of Calabi-Yau manifolds. We produce several examples by studying quotients of generalized Fermat manifolds of Calabi-Yau type. These are complete intersections of Fermat type manifolds all of the same degree and were described recently by Hidalgo, Hughes and Leyton-Álvarez. We describe all their quotients by a fixed-point-free automorphism. Most of the quotients are Log Enriques varieties or Calabi-Yau varieties with terminal singularities. In one case we get a family of Enriques manifolds which is a subfamily of a family described previously by Boissière, Camere and the third author, which is one of the two so far known families of Enriques manifolds of Calabi-Yau type. This family is obtained as an étale quotient of order two of a Calabi-Yau manifold complete intersection of quadrics, the other family is the Hilbert scheme of $n$ points on an Enriques surface. In the last part of the paper we show that these two families are different by computing their second Betti numbers, which are equal to one and eleven respectively.

math.AG↗

arXiv2026

Automorphism groups of rigid complete intersections

We study the automorphism groups of complete intersections of hypersurfaces of strictly increasing degrees in projective space. Under a combinatorial rigidity condition on the tuple of defining polynomials, we show that every automorphism of the complete intersection extends to an automorphism of each defining hypersurface, so that its automorphism group is the intersection of the automorphism groups of the defining hypersurfaces. We apply this principle to two natural families of complete intersections of two hypersurfaces of different degrees. For complete intersections of two Fermat hypersurfaces, we determine the automorphism group in every smooth case. For complete intersections of a Klein hypersurface with the reverse-order Klein hypersurface, we describe the automorphism group under an explicit arithmetic condition relating the two degrees, with Klein hypersurfaces of Wagstaff type as a natural source of examples.

math.AG↗

arXiv2026

Automorphisms of prime power order of weighted hypersurfaces

We study automorphisms of quasi-smooth hypersurfaces in weighted projective spaces, extending classical results for smooth hypersurfaces in projective space to the weighted setting. We establish effective criteria for when a power of a prime number can occur as the order of an automorphism, and we derive explicit bounds on the possible prime orders. A key role is played by a weighted analogue of the classical Klein hypersurface, which we show realizes the maximal prime order of an automorphism under suitable arithmetic conditions. Our results generalize earlier work by González-Aguilera and Liendo.

math.AG↗

arXiv2026

A one-step counterexample to the normalized Nash blowup conjecture

We construct an explicit normal singular affine toric variety X of dimension five over an algebraically closed field of characteristic three such that the normalized Nash blowup of X already contains an open affine subset isomorphic to X. Combined with previously known examples, this yields one-step counterexamples in every dimension greater than or equal to five and every characteristic. The characteristic-three case is the most delicate: the previously known counterexample in dimension four requires a two-step iteration of the normalized Nash blowup, and our example demonstrates that in dimension five and higher the minimal number of iterations needed to produce a loop is one.

math.AG↗