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EXAMPLES OF SMOOTH SURFACES IN ℙ<sup>3</sup> WHICH ARE ULRICH-WILD
Casnati, Gianfranco Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
Let $F{\subseteq}{\mathbb{P}}^3$ be a smooth surface of degree $3{\leq}d{\leq}9$ whose equation can be expressed as either the determinant of a $d{\times}d$ matrix of linear forms, or the pfaffian of a $(2d){\times}(2d)$ matrix of linear forms. In this paper we show that F supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p.
COVERS OF ALGEBRAIC VARIETIES VI. ANGLO-AMERICAN COVERS AND (1,3)-POLARIZED ABELIAN SURFACES
Casnati, Gianfranco Korean Mathematical Society 2012 대한수학회지 Vol.49 No.1
In the present paper we describe a class of Gorenstein, finite and at morphism ${\varrho}$: $X{\rightarrow}Y$ of degree 6 of algebraic varieties, called Anglo-American covers. We prove a general Bertini theorem for them and we give some evidence that the cover ${\varrho}$: $A{\rightarrow}\mathbb{P}_k^2$ associated general (1, 3)-polarized abelian surface is Anglo-American.
Examples of smooth surfaces in P3 which are Ulrich-wild
Gianfranco Casnati 대한수학회 2017 대한수학회보 Vol.54 No.2
Let $F\subseteq\mathbb{P}^3$ be a smooth surface of degree $3\le d\le 9$ whose equation can be expressed as either the determinant of a $d\times d$ matrix of linear forms, or the pfaffian of a $(2d)\times (2d)$ matrix of linear forms. In this paper we show that $F$ supports families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.
COVERS OF ALGEBRAIC VARIETIES VI. ANGLO-AMERICAN COVERS AND (1,3)-POLARIZED ABELIAN SURFACES
Gianfranco Casnati 대한수학회 2012 대한수학회지 Vol.49 No.1
In the present paper we describe a class of Gorenstein, nite and at morphism ϱ: X ! Y of degree 6 of algebraic varieties, called Anglo{American covers. We prove a general Bertini theorem for them and we give some evidence that the cover ϱ: A ! P2k associated general (1; 3){polarized abelian surface is Anglo{American.
ON THE GEOMETRY OF BIHYPERELLIPTIC CURVES
Ballico, Edoardo,Casnati, Gianfranco,Fontanari, Claudio Korean Mathematical Society 2007 대한수학회지 Vol.44 No.6
Here we consider bihyperelliptic curves, i.e., double covers of hyperelliptic curves. By applying the theory of quadruple covers, among other things we prove that the bihyperelliptic locus in the moduli space of smooth curves is irreducible and unirational $g{\geq}4{\gamma}+2{\geq}10$.