Results 1 
7 of
7
SCORZA QUARTICS OF TRIGONAL SPIN CURVES AND THEIR VARIETIES OF POWER SUMS
, 801
"... Abstract. Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and noneffective theta characteristics. This is a generalization of Mukai’s description of smooth prime Fano threefolds of genus twe ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and noneffective theta characteristics. This is a generalization of Mukai’s description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and noneffective theta characteristics. Contents
ON BLOWUPS OF THE QUINTIC DEL PEZZO 3FOLD AND VARIETIES OF POWER SUMS OF QUARTIC HYPERSURFACES
, 904
"... Abstract. We construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. This provides a generalization of Mukai’s description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. In fact in [TZ08] we show that these quar ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. This provides a generalization of Mukai’s description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. In fact in [TZ08] we show that these quartics are exactly the Scorza quartics associated to general pairs of trigonal curves and ineffective theta characteristics and this enables us to prove there the main cojecture of [DK93].
VARIETY OF POWER SUMS AND DIVISORS IN THE MODULI SPACE OF CUBIC FOURFOLDS
"... Abstract. We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums V SP (F, 10) is singular along a K3 surface of genus 20 which is the variety of power sums of a sextic curve. This relates constructions of Mukai and Iliev and Ranestad. We ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums V SP (F, 10) is singular along a K3 surface of genus 20 which is the variety of power sums of a sextic curve. This relates constructions of Mukai and Iliev and Ranestad. We also prove that these cubics form a divisor in the moduli space of cubic fourfolds and that this divisor is not a NoetherLefschetz divisor. We use this result to prove that there is no nontrivial Hodge correspondence between a very general cubic and its V SP. 1.
Contents
, 1998
"... 2. Auxiliary flips and back tracking method 3. Set up and dividing into cases ..."
Abstract
 Add to MetaCart
2. Auxiliary flips and back tracking method 3. Set up and dividing into cases