»ã±¨±êÌâ (Title)£ºEffective Gonality Theorem£¨ÓÐЧÕý½»ÐÔ¶¨Àí£©

»ã±¨ÈË (Speaker)£ºÅ£ÎIJ© ½ÌÊÚ£¨ÃÀ¹ú°¢¿ÏÉ«´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê6ÔÂ10ÈÕ (Öܶþ)15:40-16:40

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»ã±¨ÌáÒª£ºÔÚÕâÒ»½²ÖУ¬ÎÒ½«»áÉÌÓÐЧÕý½»ÐÔ¶¨Àí¡£1986Ä꣬Green-LazarsfeldÌá³öÁËgonality²Â²â£¬ÒÔΪ¹â»¬Í¶Ó°ÇúÏßµÄgonalityÄܹ»´ÓÇúÏßÉÏÒ»¸ö×ã¹»ÕýµÄÏßÊøµÄȨһºÏ¼¯Öеõ½¡£ËûÃÇ»¹Ìá³öÁËÕâÖÖÏßÊø¿ÉÄÜ´æÔÚµÄ×îÓ×ˮƽ¡£2015Ä꣬Ein- LazarsfeldÖ¤ÁËÈ»×ã¹»´ó¶ÈÏßÊøµÄ²Â²â£¬µ«¸Ã²Â²âµÄÓÐЧ²¿ÃÅÒÀÈ»¿í·ºÊ¢¿ª£¬²¢ÓÉFarkas-Kemeny³ÁÐÂÃ÷È·±íÊö¡£ÔÚ±¾ÎÄÖУ¬ÎÒÃdzÉÁ¢ÁËȨһºÏ×ÓµÄÓÐЧÒþû¶¨Àí£¬ËüÔ̺­ÁËÓÐЧµÄÕý½»ÐԲ²â¡£ÕâÏî×êÑÐÊÇÓëJinhyung Parkһ·ºÏ×÷»ñµÃµÄ¡£

Abstract£ºIn this talk, I will discuss effective result for gonality theorem. In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality of a smooth projective curve can be read off from weight-one syzygies of a sufficiently positive line bundle on the curve. They also proposed possible least degree of such a line bundle. In 2015, Ein--Lazarsfeld proved the conjecture for line bundles of sufficiently large degree, but the effective part of the conjecture remained widely open and was reformulated explicitly by Farkas-Kemeny. In this talk, we establish an effective vanishing theorem for weight-one syzygies, which implies the effective gonality conjecture. This is a joint work with Jinhyung Park.