1,721,029 research outputs found
The Poicaré series of a local Gorenstein ring of multiplicity up to 10 is rational
No full textWe prove the rationality of the Poincaré series for a certain class of local Gorenstein rings
On some Gorenstein loci in Hilb_6(P^4_k)
No full textLet be an algebraically closed field and let \Hilb_{d}^{aG}(\p{d-2}) be the open locus inside the Hilbert scheme \Hilb_{d}(\p{d-2}) corresponding to arithmetically Gorenstein subschemes. We prove the irreducibility and characterize the singularities of \Hilb_{6}^{aG}(\p{4}). In order to achieve these results we also classify all Artinian, Gorenstein, not necessarily graded, --algebras up to degree . Moreover we describe the loci in \Hilb_{6}^{aG}(\p{4}) obtained via some geometric construction. Finally we prove the obstructedness of some families of points in \Hilb_{d}^{aG}(\p{d-2}) for each $d\ge6
On the Gorenstein locus of the punctual Hilbert scheme of degree 11
Full text linkLet k be an algebraically closed field of characteristic 0 and let Hilb_d^G(P_k^N) be the open locus of the Hilbert scheme Hilb_d(P_k^N) corresponding to Gorenstein subschemes. We proved in several previous papers that Hilb_d^G(P_k^N) is irreducible for d⩽10 and N⩾1, characterizing its singular locus. In the present paper we prove that also Hilb_{11}^G(P_k^N) is irreducible for each N⩾1. We also give some results about its singular locus
Regiospecific Reactions of Phenol Salts: Reaction-Pathways of Alkylphenoxymagnesiumhalides with Triethylorthoformate
No full textThe moduli spaces of bielliptic curves of genus 4 with more bielliptic structures
No full textLet be an irreducible, smooth, projective curve of genus over the complex field . The curve is called {\sl bielliptic}\/ if it admits a degree two morphism onto an elliptic curve : such a morphism is called a {\sl bielliptic structure}\/ on . If is bielliptic and then the bielliptic structure on is unique, but if this holds true only generically and there are curves carrying bielliptic structures. We have the sharp bounds for respectively. Let be the coarse moduli space of irreducible, smooth, projective curves of genus . We denote by the locus of points in representing curves carrying at least bielliptic structures. It is then natural to ask the following questions. Clearly : does hold? What are the irreducible components of ? Are the irreducible components of rational? How do the irreducible components of intersect each other? Let : how many non-isomorphic elliptic quotient can it have? In the present paper we give complete answers to the above questions in the case $g=4
On the irriducibility and singularities of the Gorenstein locus of the punctual Hilbert scheme of degree 10
No full textLet be an algebraically closed field of characteristic and let \Hilb_{d}^{G}(\p{N}) be the open locus of the Hilbert scheme \Hilb_{d}(\p{N}) corresponding to Gorenstein subschemes. We proved in a previous paper that \Hilb_{d}^{G}(\p{N}) is irreducible for and . In the present paper we prove that also \Hilb_{10}^{G}(\p{N}) is irreducible for each , giving also a complete description of its singular locu
The rationality of the Weierstrass space of type (4,g)
No full textLet \M_g be the moduli space of smooth, integral curves of genus over
the complex field .
We denote by the locus inside \M_g of --gonal curves with exactly one total ramification point, the other
ramification points being simple. is
irreducible of dimension
. Moreover for it is also unirational. It is then a natural question to ask whether is
also rational for this values of . The locus
is the hyperelliptic locus and F\. Bogomolov and P\.
Katsylo proved its rationality for any . More recently we proved that
is rational too when .
In the present paper we prove that is also rational when
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