Authors:Wahei Hara Pages: 3 - 24 Abstract: In this paper, we study the derived category of certain toric va- rieties with Picaed number three which are blowing-up another toric varieties along their torus invariant loci of codimension at most three. We construct strong full exceptional collections by using Orlov’s blow-up formula and mu- tations. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Sepideh Tashvighi Pages: 25 - 31 Abstract: We further analyse the moduli space of stable curves with level structure provided by Chiodo and Farkas in [2]. Their result builds upon Harris and Mumford analysis of the locus of singularities of the moduli space of curves and shows in particular that for levels 2, 3, 4, and 6 the locus of noncanonical singularities is completely analogous to the locus described by Harris and Mumford, it has codimension 2 and arises from the involution of elliptic tails carrying a trivial level structure. For the remaining levels (5, 7, and beyond), the picture also involves components of higher codimension. We show that there exists a component of codimension 3 for levels ℓ = 5 and ℓ > 7 with the only exception of level 12. We also show that there exists a component of codimension 4 for ℓ = 12. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Seyed Zoalroshd Pages: 33 - 36 Abstract: In this short note we give a universal inequality between the largest eigenvalue of the Riesz potentials and non-zero Neumann eigenvalue for domains on hemispheres of S^n PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Alberto Calabri, Ezio Stagnaro Pages: 37 - 68 Abstract: We show how to construct some old and new surfaces of general typewith vanishing geometric genus from double planes,by computing explicit equations of their branch curves. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Masahiro Ohno Pages: 69 - 81 Abstract: We describe nef vector bundles on a projective space with first Chern class three and second Chern class eight over an algebraically closed field of characteristic zero by giving them a minimal resolution in terms of a full strong exceptional collection of line bundles. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Giuseppe Zito Pages: 83 - 86 Abstract: In this paper we provide an elementary and easy proof that a proper subalgebra of the matrix algebra K^n,n, with n>=3 and K an arbitrary field, has dimension strictly less than n^2-1 PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Shin-Yao Jow, Adrien SAUVAGET, Hacen ZELACI Pages: 87 - 98 Abstract: In this paper, we study principally polarized abelian varieties X of dimension g with a curve C such that the class of C is m times the minimal class. Welters introduced the formalism of complementary pairs to handle this problem in the case m = 2. We generalize the results of Welters and construct families of principally polarized abelian varieties for any m and compute the dimension of the locus of these abelian varieties. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Alice Cuzzucoli, Riccardo Moschetti, Maiko Serizawa Pages: 99 - 114 Abstract: Consider the projection of a smooth irreducible surface in $\P^3$ from a point. The uniform position principle implies that the monodromy group of such a projection from a general point in $\P^3$ is the whole symmetric group. We will call such points uniform. Inspired by a result of Pirola and Schlesinger for the case of curves, we proved that the locus of non-uniform points of $\P^3$ is at most finite. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Ananyo Dan, Mohamad Zaman Fashami, Natascia Zangani Pages: 115 - 129 Abstract: In this article, we study subloci of solvable curves in Mg which are contained in either a K3-surface or a quadric or a cubic surface. We give a bound on the dimension of such subloci. In the case of complete intersection genus g curves in a cubic surface, we show that a general such curve is solvable. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Roberto Laface, Cèsar Martìnez Pages: 131 - 140 Abstract: We prove an extension of the Babbage-Enriques-Petri theorem for semi-canonical curves. We apply this to show that the Prym variety of a generic element of a codimension $k$ subvariety of $\kr_g$ is not isogenous to another distinct Prym variety, under some mild assumption on $k$. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Sammy Alaoui Soulimani, Paola Porru Pages: 141 - 154 Abstract: We construct two divisors in the moduli space $\mathcal{A}_4 ^{(1,1,2,2)}$ and we check their invariance and non-invariance under the canonical involution introduced by C. Birkenhake and H. Lange. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Sara Torelli, Filippo Francesco Favale Pages: 155 - 182 Abstract: Motivated by a conjecture of Xiao, we study families of coverings of elliptic curves and their corresponding Prym map . More precisely, we describe the codi↵erential of the period map P associated to in terms of the residue of meromorphic 1-forms and then we use it to give a characterization for the coverings for which the dimension of Ker(dP) is the least possibile. This is useful in order to exclude the existence of non isotrivial fibrations with maximal relative irregularity and thus also in order to give counterexamples to the Xiao’s conjecture mentioned above. The first counterexample to the original conjecture, due to Pirola, is then analysed in our framework. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
Authors:Luca Rizzi, Federico Caucci, Yonghwa Cho Pages: 183 - 194 Abstract: Let S be a very general complete intersection surface of multidegree (d_1,d_2) in P^4. The following problem arises: determine the couples (d_1,d_2) such that the surface S does not have any "non-evident" rational map to other surfaces. By non-evident rational map, we mean non-birational dominant map whose target space is not rational. We give a partial solution, presenting a class of multidegrees (d_1,d_2) which satisfy the above condition. PubDate: 2017-11-15 Issue No:Vol. 72, No. 2 (2017)
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